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Algorithmic Combinatorics Publications

Type: [any] [Papers] [Theses] [Technical Reports] [Other
Author: [any] [Paule] [Kauers] [Koutschan] [Pillwein] [Radu] [Riese] [Schneider] [Stan] [Zimmermann
Year: [any] [2010] [2009] [2008] [2007] [2006] [2005] [earlier

Alin Bostan, Manuel Kauers. The Complete Generating Function for Gessel Walks is Algebraic. Proceedings of the AMS, pp. ?-?. 2010. ISSN 0002-9939. to appear. [pdf] [ps] [bib]
Christoph Koutschan. HolonomicFunctions (User's Guide). Technical report no. 10-01 in RISC Report Series, University of Linz, Austria. January 2010. [url] [pdf] [bib]
Christoph Koutschan, Manuel Kauers, Doron Zeilberger. A Proof of George Andrews' and David Robbins' q-TSPP-Conjecture. ArXiv. Technical report no. 1002.4384, 2010. [pdf] [ps] [bib]
C. Schneider. Parameterized Telescoping Proves Algebraic Independence of Sums. Ann. Comb., pp. ?-. 2010. ISSN 0218-0006.. To appear. [pdf] [bib]
C. Schneider. A Symbolic Summation Approach to Find Optimal Nested Sum Representations. In: Proceedings of the Conference on Motives, Quantum Field Theory, and Pseudodifferential Operators, , To appear in the Mathematics Clay Proceeding , pp. -. 2010. arXiv:0808.2543. [pdf] [bib]
C. Schneider. Structural Theorems for Symbolic Summation. Appl. Algebra Engrg. Comm. Comput. 21(1), pp. 1-32. 2010. ISSN 0938-1279. [pdf] [bib]
Jakob Ablinger. A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics. Johannes Kepler University. Diploma Thesis. February 2009. [pdf] [bib]
Buchberger, B.; Affenzeller, M.; Ferscha, A.; Haller, M.; Jebelean, T.; Klement, E.P.; Paule, P.; Pomberger, G.; Schreiner, W.; Stubenrauch, R.; Wagner, R.; Weiß, G.; Windsteiger, W.. Hagenberg Research. 1st edition, 2009. Springer Dordrecht Heidelberg London New York, 488 pages, ISBN 978-3-642-02126-8. [url] [bib]
Peter Paule, Bruno Buchberger, Lena Kartashova, Manuel Kauers, Carsten Schneider, Franz Winkler. Algorithms in Symbolic Computation. In: Hagenberg Research, Bruno Buchberger et al. (ed.), Chapter 1, pp. 5-62. 2009. Springer, 978-3-642-02126-8. [pdf] [bib]
Manuel Kauers. Guessing Handbook. Technical report no. 09-07 in RISC Report Series, University of Linz, Austria. 2009. [nb] [pdf] [bib]
Frederic Chyzak, Manuel Kauers, Bruno Salvy. A Non-Holonomic Systems Approach to Special Function Identities. In: Proceedings of ISSAC'09, John May (ed.), pp. 111-118. 2009. 978-1-60558-609-0. [pdf] [ps] [bib]
Alin Bostan, Manuel Kauers. Automatic Classification of Restricted Lattice Walks. In: Proceedings of FPSAC'09, Christian Krattenthaler, Volker Strehl, and Manuel Kauers (ed.), pp. 201-215. 2009. [ps] [pdf] [bib]
Manuel Kauers, Christoph Koutschan. A Mathematica Package for q-Holonomic Sequences and Power Series. The Ramanujan Journal 19(2), pp. 137-150. 2009. Springer, ISSN 1382-4090. [pdf] [ps] [bib]
Manuel Kauers, Christoph Koutschan, Doron Zeilberger. A Proof of George Andrews' and Dave Robbins' q-TSPP-Conjecture (modulo a finite amount of routine calculations). The personal Journal of Ekhad and Zeilberger, pp. 1-8. January 2009. [url] [pdf] [ps] [bib]
Manuel Kauers, Christoph Koutschan, Doron Zeilberger. Proof of Ira Gessel's Lattice Path Conjecture. Proceedings of the National Academy of Sciences 106(28), pp. 11502-11505. July 2009. ISSN 0027-8424. [ps] [pdf] [bib]
Christoph Koutschan. Eliminating Human Insight: An Algorithmic Proof of Stembridge's TSPP Theorem. RISC, JKU Linz. Technical report no. arXiv:0906.1018, 2009. [pdf] [bib]
Christoph Koutschan. Advanced Applications of the Holonomic Systems Approach. RISC-Linz, Johannes Kepler University. PhD Thesis. September 2009. [url] [pdf] [bib]
Karin Nachbagauer. Power Series Solutions to Holonomic Differential Equations and the General Algebraic Equation. Johannes Kepler University Linz. Diploma Thesis. 2009. The thesis also appeared as RISC report 09-15.. Diploma thesis. [pdf] [bib]
Peter Paule, Silviu Radu. A Proof of Sellers' Conjecture. RISC. Technical report no. 09-17, 2009. [pdf] [bib]
Peter Paule, Silviu Radu. Infinite Families of Strange Partition Congruences for Broken 2-diamonds. RISC. Technical report no. 09-18, 2009. [pdf] [bib]
D. Braess, V. Pillwein, J. Schöberl. Equilibrated Residual Error Estimates are $p$-Robust. Comput. Methods Appl. Mech. Engrg. 198, pp. 1189-1197. 2009. [ps] [pdf] [bib]
J. Kraus, V. Pillwein, L. Zikatanov. Algebraic multilevel iteration methods and the best approximation to 1/x in the uniform norm. RICAM. Technical report no. 2009-17, 2009. [pdf] [ps] [bib]
C. Schneider, R. Osburn. Gaussian Hypergeometric series and supercongruences. Math. Comp. 78(267), pp. 275-292. 2009. ISSN 0025-5718. [url] [pdf] [bib]
J. Bluemlein, M. Kauers, S. Klein, C. Schneider. From moments to functions in higher order QCD . In: Proc. of Science, - (ed.), Proceedings of XII Advanced Computing and Analysis Techniques in Physics Research PoS(ACAT08)106, pp. 1-7. 2009. ISSN 1824-8039. [pdf] [bib]
J. Bluemlein, M. Kauers, S. Klein, C. Schneider. Determining the closed forms of the {$O(a_s^3)$} anomalous dimensions and {W}ilson coefficients from {M}ellin moments by means of computer algebra. Comput. Phys. Comm. 180, pp. 2143-2165. 2009. ISSN 0010-4655. [pdf] [bib]
Flavia Stan. Computer-Assisted Proofs of Special Function Identities Related to Poisson Integrals. The Ramanujan Journal 20(1), pp. 55-67. 2009. Springer, ISSN 1382-4090. [bib]
Karen T. Kohl and Flavia Stan. An Algorithmic Approach to the Mellin Transform Method. Doctoral Program Computational Mathematics. Technical report no. DK-2009-03, November 2009. To appear in Contemporary Mathematics. [pdf] [bib]
Manuela Wiesinger. Contributions to MacMahon's Partition Analysis. Technical report no. 09-05 in RISC Report Series, University of Linz, Austria. January 2009. Master Thesis. [pdf] [bib]
Manuela Wiesinger. Contributions to MacMahon's Partition Analysis. Johannes Kepler University. Diploma Thesis. January 2009. RISC Report 09-05. [pdf] [bib]
Manuel Kauers, Doron Zeilberger. Experiments with a Positivity Preserving Operator. Experimental Mathematics 17(3), pp. 341-345. 2008. ISSN 1058-6458. [pdf] [ps] [bib]
Manuel Kauers. Solving Difference Equations whose Coefficients are not Transcendental. Theoretical Computer Science 401(1-3), pp. 217-227. July 2008. ISSN 0304-3975. [pdf] [ps] [bib]
Manuel Kauers, Doron Zeilberger. The Quasi-Holonomic Ansatz and Restricted Lattice Walks. Journal of Difference Equations and Applications 14(10-11), pp. 1119-1126. 2008. ISSN 1023-6198. to appear. [pdf] [ps] [bib]
Manuel Kauers. Integration of Algebraic Functions: A Simple Heuristic for Finding the Logarithmic Part. In: Proceedings of ISSAC'08, David Jeffrey (ed.), Proceedings of ISSAC'08, pp. 133-140. 2008. 978-1-59593-904-3. [ps] [pdf] [bib]
Manuel Kauers. Computer Algebra for Special Function Inequalities. In: Tapas in Experimental Mathematics, Tewodros Amdeberhan, Victor Moll (ed.), Contemporary Mathematics 457, pp. 215-235. 2008. AMS, ISBN 978-0-8218-4317-8. [pdf] [ps] [bib]
Manuel Kauers. Fast Solvers for Dense Linear Systems. Nuclear Physics B (Proc. Suppl.) 183, pp. 245-250. 2008. ISSN 0550-3213. [ps] [pdf] [bib]
Christoph Koutschan. Regular Languages and Their Generating Functions: The Inverse Problem. Theoretical Computer Science 391(1-2), pp. 65-74. 2008. ISSN 0304-3975. [pdf] [ps] [bib]
Christoph Koutschan, Viktor Levandovskyy. Computing one of Victor Moll's irresistible integrals with computer algebra. Computer Science Journal of Moldova 16(1(46)), pp. 35-49. 2008. ISSN 1561-4042. [pdf] [bib]
Peter Paule. Henrici's Friendly Monster Identity Revisited. Technical report no. 08-19 in RISC Report Series, University of Linz, Austria. December 2008. Dedicated to Professor Georgy Egorychev on the occasion of his 70th birthday. [pdf] [bib]
P. Paule, V. Pillwein. Automatic Improvements of Wallis' Inequality. Technical report no. 08-18 in RISC Report Series, University of Linz, Austria. 2008. [pdf] [ps] [bib]
William Y. C. Chen, Peter Paule, Husam L. Saad. Converging to Gosper's Algorithm. Technical report no. 08-20 in RISC Report Series, University of Linz, Austria. December 2008. [pdf] [bib]
S. Beuchler, V. Pillwein. Completions to sparse shape functions for triangular and tetrahedral p-FEM. In: Domain Decomposition Methods in Science and Engineering XVII, U. Langer and M. Discacciati and D.E. Keyes and O.B. Widlund and W. Zulehner (ed.), Lecture Notes in Computational Science and Engineering 60, pp. 435-442. 2008. Springer, Heidelberg, [pdf] [bib]
V. Pillwein. Positivity of certain sums over Jacobi kernel polynomials. Adv. in Appl. Math. 41(3), pp. 365-377. 2008. doi:10.1016/j.aam.2007.12.001. [pdf] [ps] [bib]
Veronika Pillwein. Computer Algebra Tools for Special Functions in High Order Finite Element Methods. Johannes Kepler University Linz. PhD Thesis. 2008. [ps] [pdf] [bib]
C. Schneider. A Refined Difference Field Theory for Symbolic Summation. J. Symbolic Comput. 43(9), pp. 611-644. 2008. ISSN 0747-7171. [pdf] [bib]
Manuel Kauers , Carsten Schneider. Automated Proofs for Some Stirling Number Identities. The Electronic Journal of Combinatorics 15(1), pp. 1-7. 2008. ISSN 1077-8926. R2. [pdf] [ps] [bib]
M. Kuba, H. Prodinger, C. Schneider. Generalized Reciprocity Laws for Sums of Harmonic Numbers. INTEGERS. Electronic Journal of Combinatorial Number Theory 8(A17), pp. 1-20. 2008. ISSN 1553-1732. [url] [pdf] [bib]
I. Bierenbaum, J. Bluemlein, S. Klein, C. Schneider. Two-Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O!(epsilon)$. Nucl.Phys. B 803(1-2), pp. 1-41. November 2008. ISSN: 0550-3213. [url] [pdf] [bib]
Flavia Stan. Computer-Assisted Proofs of Special Function Identities Related to Poisson Integrals. SFB F13. Technical report no. 2008-3, January 2008. [ps] [pdf] [bib]
S. Gerhold, L. Glebsky, C. Schneider, H. Weiss, B. Zimmermann. Computing the complexity for schelling segregation models. Communications in Nonlinear Science and Numerical Simulations 13, pp. 2236-2245. 2008. ISSN 1007-5704. [pdf] [bib]
Manuel Kauers, Burkhard Zimmermann. Computing the Algebraic Relations of C-finite Sequences and Multisequences. Journal of Symbolic Computation 43(11), pp. 787-803. 2008. ISSN 0747-7171.. [pdf] [ps] [bib]
J.P. Bell, S. Gerhold. On the Positivity Set of a Linear Recurrence Sequence.. Israel J. Math. 157, pp. 333-345. 2007. 'ISSN' 0021-2172. [bib]
J.P. Bell, S. Gerhold, M. Klazar, F. Luca. Non-Holonomicity of Sequences defined via Elementary Functions.. Annals of Combinatorics, pp. ?-. 2007. 'ISSN' 0218-0006. To appear.. [bib]
Manuel Kauers. Computer Algebra and Power Series with Positive Coefficients. In: Proceedings of FPSAC'07, , pp. 1-7. 2007. [pdf] [ps] [bib]
Manuel Kauers, Peter Paule. A Computer Proof of Moll's Log-Concavity Conjecture. Proceedings of the AMS 135(12), pp. 3847-3856. December 2007. ISSN 0002-9939. to appear. [ps] [bib]
Horst Alzer, Stefan Gerhold, Manuel Kauers, Alexandru Lupas. On Turan's Inequality for Legendre Polynomials. Expositiones Mathematicae 25(2), pp. 181-186. May 2007. ISSN 0723-0869. [pdf] [ps] [bib]
Manuel Kauers. An Algorithm for Deciding Zero Equivalence of Nested Polynomially Recurrent Sequences. Transactions on Algorithms 3(2), pp. 1-13. 2007. 1549-6325. article 18. [pdf] [ps] [bib]
Manuel Kauers, Manfred Kerber, Robert Miner, Wolfgang Windsteiger (ed.). Towards Mechanized Mathematical Assistants. Proceedings of Calculemus 2007 and MKM 2007, Lecture Notes in Computer Science, 4573, 2007. Springer, Heidelberg, ISSN 0302-9743. [url] [bib]
Manuel Kauers, Manfred Kerber, Robert Miner, Wolfgang Windsteiger. Calculemus/MKM 2007 - Work in Progress. Technical report no. 07-06 in RISC Report Series, University of Linz, Austria. 2007. [pdf] [ps] [bib]
Manuel Kauers. Summation Algorithms for Stirling Number Identities. Journal of Symbolic Computation 42(10), pp. 948-970. October 2007. ISSN 0747-7171. [pdf] [ps] [bib]
Herwig Hauser, Christoph Koutschan. Linear Recurrences and Power Series Division. SFB F013. Technical report no. 2007-20, Johannes Kepler University, A-4040 Linz, 2007. [ps] [pdf] [bib]
F. Chyzak, P. Paule. Computer Algebra. In: The Digital Library of Mathematical Functions (DLMF), D. Lozier (ed.), pp. n/a-n/a. 2007. National Institute of Standards and Technology (NIST), Gaithersburg, U.S.A., electronic. In preparation. [bib]
George E. Andrews, Peter Paule. MacMahon's Partition Analysis XI: Broken diamonds and modular forms. Acta Arith. 126, pp. 281-294. 2007. ISSN 0065-1036. [bib]
G. E. Andrews and P. Paule. MacMahon's Partition Analysis XII: Plane Partitions. Journal of the London Mathematical Society 76(3), pp. 647-666. 2007. London Mathematical Society, 0024-6107. [bib]
S. Beuchler, V. Pillwein. Sparse shape functions for tetrahedral $p$-FEM using integrated Jacobi polynomials. Computing 80(4), pp. 345-375. 2007. [ps] [pdf] [bib]
C. Schneider, R. Pemantle. When is 0.999... equal to 1?. Amer. Math. Monthly 114(4), pp. 344-350. 2007. ISSN 0002-9890. Preliminary version online. [ps] [pdf] [bib]
C. Schneider. Simplifying Sums in ${\Pi}{\Sigma}^*$-Extensions. J. Algebra Appl. 6(3), pp. 415-441. 2007. ISSN: 0219-4988. Preliminary version online. [ps] [pdf] [bib]
C. Schneider. Symbolic Summation Assists Combinatorics. Sem. Lothar. Combin. 56, pp. 1-36. 2007. ISSN 1286-4889. Article B56b. [url] [ps] [pdf] [bib]
C. Schneider. {A}p\'{e}ry's Double Sum is Plain Sailing Indeed. Electron. J. Combin. 14(N5), pp. 1-3. 2007. ISSN 1077-8926. [url] [ps] [pdf] [bib]
M. Kauers, C. Schneider. Symbolic Summation with Radical Expressions. In: Proceedings of ISSAC'07, Christopher W. Brown (ed.), pp. 219-226. 2007. isbn 978-1-59593-743-8. [pdf] [ps] [bib]
P. Paule, C. Schneider. Truncating Binomial Series with Symbolic Summation. INTEGERS. Electronic Journal of Combinatorial Number Theory 7(A22), pp. 1-9. 2007. ISSN 1553-1732. [url] [pdf] [bib]
C. Schneider. Parameterized telescoping proves algebraic independence of sums. 2007. Poster presentation at FPSAC 2007. [url] [pdf] [pdf] [bib]
I. Bierenbaum, J. Blümlein, S. Klein, C. Schneider. Difference equations in massive higher order calculations. In: Proc. ACAT 2007, - (ed.)PoS(ACAT)082, pp. 1-15. 2007. ISSN 18248039. [url] [pdf] [bib]
S. Moch, C. Schneider. Feynman integrals and difference equations. In: Proc. ACAT 2007, - (ed.)PoS(ACAT)083, pp. 1-11. 2007. ISSN 18248039. [url] [pdf] [bib]
Flavia Stan. On Recurrences for Ising Integrals. SFB F13. Technical report no. 2007-32, December 2007. To appear in Adv. Appl. Math.. [ps] [pdf] [bib]
Stefan Gerhold, Manuel Kauers. A Computer Proof of Turan's Inequality. Journal of Inequalities in Pure and Applied Mathematics 7(2), pp. 1-4. May 2006. Article 42. [ps] [bib]
Manuel Kauers. SumCracker - A Package for Manipulating Symbolic Sums and Related Objects. Journal of Symbolic Computation 41(9), pp. 1039-1057. 2006. ISSN 0747-7171. [pdf] [ps] [bib]
Manuel Kauers. Shift Equivalence of P-finite Sequences. The Electronic Journal of Combinatorics 13(1), pp. 1-16. 2006. ISSN 1077-8926. R100. [pdf] [ps] [bib]
Manuel Kauers. Computer Algebra and Power Series with Positive Coefficients. SFB F013. Technical report no. 2006-33, Altenbergerstrasse 69, November 2006. [pdf] [ps] [bib]
Manuel Kauers. Problem 11258. December 2006. American Mathematical Monthly, [ps] [bib]
V. Levandovskyy. Intersection of Ideals with Non-commutative Subalgebras. J. Kepler University Linz. Technical report no. 2006-14, April 2006. the final version has been accepted for the Proceedings ISSAC 2006. SFB Report. [pdf] [bib]
V. Levandovskyy. PLURAL, a Non-commutative Extension of SINGULAR: Past, Present and Future. In: Mathematical Software - ICMS 2006, A. Iglesias, N. Takayama (ed.), Proceedings of International Congress on Mathematical Software, LNCS 4151, pp. 144-157. September 2006. 0302-9743. [pdf] [bib]
V. Levandovskyy. Intersection of Ideals with Non-commutative Subalgebras. In: Proceedings of the ISSAC 2006 Conference, Jean-Guillaume Dumas (ed.), Proceedings of ISSAC 2006, pp. 212-219. July 2006. ACM Press, 1-59593-095-7. [bib]
V. Levandovskyy, E. Zerz. Algebraic systems theory and computer algebraic methods for some classes of linear control systems. In: Proc. of the International Symposium on Mathematical Theory of Networks and Systems (MTNS'06), Y. Yamamoto (ed.), Proceedings of International Symposium on Mathematical Theory of Networks and Systems (MTNS'06), pp. -. July 2006. 1234-8765. [pdf] [bib]
Manuel Kauers, Viktor Levandovskyy. An Interface between Mathematica and Singular. SFB F013. Technical report no. 2006-29, 2006. [pdf] [ps] [bib]
G. E. Andrews, P. Paule. MacMahon's Dream. SFB 013. Technical report, September 2006. SFB-report 2006-26. [pdf] [bib]
G. E. Andrews, P. Paule. MacMahon's Partition Analysis XI: The Search for Modular Forms. SFB 013. Technical report, 2006. SFB-report 2006-27. [pdf] [bib]
G. E. Andrews, P. Paule. MacMahon's Partition Analysis XII: Plane Partitions. SFB 013. Technical report, September 2006. SFB-report 2006-28. [pdf] [bib]
A. Becirovic, P. Paule, V. Pillwein, A. Riese, C. Schneider, J. Schöberl. Hypergeometric Summation Algorithms for High Order Finite Elements. Computing 78(3), pp. 235-249. 2006. ISSN 0010-485X. Preliminary version available. [pdf] [ps] [bib]
K. Driver, H. Prodinger, C. Schneider, A. Weideman. Pad'e Approximations to the logarithm II: Identities, recurrences, and symbolic computation. Ramanujan Journal 11(2), pp. 139-158. April 2006. ISSN 1382-4090. Preliminary version online. [url] [pdf] [ps] [bib]
K. Driver, H. Prodinger, C. Schneider, A. Weideman. Pad'e approximations to the logarithm III: Alternative methods and additional results. Ramanujan Journal 12(3), pp. 299-314. 2006. ISSN 1382-4090. Preliminary version online. [ps] [pdf] [ps] [bib]
C. Schneider. Some notes on ``When is 0.999... equal to 1?''. In: Mathematics, Algorithms, Proofs, T. Coquand et al. (ed.), Dagstuhl Seminar Proceedings 05021, pp. 1-3. 2006. Internationales Begegnungs- und Forschungszentrum (IBFI), Schloss Dagstuhl, Germany, ISSN 1862-4405. [url] [pdf] [bib]
M. Kauers, C. Schneider. Indefinite summation with unspecified summands. Discrete Math. 306(17), pp. 2073-2083. 2006. ISSN 0012-365X. Preliminary version online. [pdf] [bib]
M. Kauers, C. Schneider. Application of unspecified sequences in symbolic summation. In: Proceedings of ISSAC'06, Jean-Guillaume Dumas (ed.), Proceedings of ISSAC'06, pp. 177-183. 2006. ACM Press, [pdf] [ps] [bib]
P. Paule, V. Pillwein, C. Schneider, J. Schöberl. Hypergeometric Summation Techniques for High Order Finite Elements. In: PAMM, , Proceedings of GAMM Annual Meeting 2006 - Berlin6/1, pp. 689-690. 2006. Wiley InterScience, Weinheim, ISBN. DOI: 10.1002/pamm.200610325. [bib]
Stefan Gerhold, Manuel Kauers, Joachim Schoeberl. On a Conjectured Inequality for a Sum of Legendre Polynomials. SFB F013. Technical report, April 2006. [ps] [bib]
George E. Andrews, Arnold Knopfmacher, Burkhard Zimmermann. On the number of distinct multinomial coefficients. Journal of Number Theory 118(1), pp. 15-30. May 2006. ISSN 0022-314X. [pdf] [bib]
P. Flajolet, S. Gerhold, B. Salvy. On the non-holonomic character of logarithms, powers and the nth prime function. Electronic Journal of Combinatorics 11(2), pp. 1-16. 2005. ISSN 1077-8926. [pdf] [bib]
S. Gerhold. Point Lattices and Oscillating Recurrence Sequences. Journal of Difference Equations and Applications 11(6), pp. 515-533. 2005. ISSN 1023-6198. [pdf] [bib]
S. Gerhold. Combinatorial Sequences: Non-Holonomicity and Inequalities. RISC, J. Kepler University Linz. PhD Thesis. August 2005. [pdf] [bib]
J. P. Bell, S. Gerhold. The Positivity Set of a Recurrence Sequence. J. Kepler University Linz. Technical report, to appear in Israel J. Math., 2005. SFB report. [pdf] [bib]
Stefan Gerhold, Manuel Kauers. A Procedure for Proving Special Function Inequalities Involving a Discrete Parameter. In: Proceedings of ISSAC '05, Manuel Kauers (ed.), pp. 156-162. 2005. ACM Press, ISBN 1-59593-095-705/0007. [ps] [bib]
Manuel Kauers. Algorithms for Nonlinear Higher Order Difference Equations. RISC-Linz. PhD Thesis. October 2005. [ps] [ps] [bib]
Christoph Koutschan. Regular Languages and Their Generating Functions: The Inverse Problem. Friedrich-Alexander-Universität Erlangen-Nürnberg. Diploma Thesis. August 2005. [url] [pdf] [bib]
V. Levandovskyy, E. Zerz. Computer algebraic methods for the structural analysis of linear control systems. Proceedings in Applied Mathematics and Mechanics (PAMM) 5(1), pp. 717-718. 2005. WILEY-VCH, ISSN 1617-7061. DOI: 10.1002/pamm.200510333. [pdf] [bib]
P. Paule. A Computerized Proof of $\zeta(2)=\pi^2/6$. 2005. in preparation. [bib]
C. Schneider. Product Representations in $\Pi\Sigma$-Fields. Annals of Combinatorics 9(1), pp. 75-99. 2005. ISSN 0218-0006. Preliminary version online. [ps] [pdf] [bib]
C. Schneider. A new Sigma approach to multi-summation. Advances in Applied Math. Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud 34(4), pp. 740-767. 2005. ISSN 0196-8858. Preliminary version online. [pdf] [ps] [bib]
G. E. Andrews, P. Paule, C. Schneider. Plane Partitions VI: Stembridge's TSPP Theorem. Advances in Applied Math. Special Issue Dedicated to Dr. David P. Robbins. Edited by D. Bressoud 34(4), pp. 709-739. 2005. ISSN 0196-8858. Preliminary version online. [pdf] [ps] [bib]
C. Schneider. Degree Bounds To Find Polynomial Solutions of Parameterized Linear Difference Equations in $\Pi\Sigma$-Fields. Appl. Algebra Engrg. Comm. Comput. 16(1), pp. 1-32. 2005. ISSN 0938-1279. Preliminary version online. [pdf] [ps] [bib]
C. Schneider. Solving Parameterized Linear Difference Equations in Terms of Indefinite Nested Sums and Products. J. Differ. Equations Appl. 11(9), pp. 799-821. 2005. ISSN 1023-6198. Preliminary version online. [ps] [pdf] [bib]
C. Schneider. Finding Telescopers with Minimal Depth for Indefinite Nested Sum and Product Expressions (Extended Version). J. Kepler University Linz. Technical report no. 2005-08, 2005. SFB-Report. [ps] [pdf] [bib]
C. Schneider. Finding Telescopers with Minimal Depth for Indefinite Nested Sum and Product Expressions. In: Proc. ISSAC'05, M. Kauers (ed.), pp. 285-292. 2005. ACM, ISBN 1-59593-095-705/0007. [pdf] [ps] [bib]
M. Semrad. Special Functions, Computer Proofs and the DLMF. RISC, J. Kepler University Linz. Diploma Thesis. 2005. [bib]
Burkhard Zimmermann. Computing Recurrences for Parameter-Dependent Integrals. May 2005. Poster presentation at Fourth International School on Computer Algebra CoCoA 4. [bib]
S. Gerhold. On Some Non-Holonomic Sequences. Electronic Journal of Combinatorics 11(1), pp. 1-8. 12 2004. RISC, J. Kepler University Linz, ISSN 1077-8926. [url] [pdf] [tex] [ps] [bib]
Manuel Kauers. Computer Proofs for Polynomial Identities in Arbitrary Many Variables. In: Proceedings of ISSAC 2004, Jaime Gutierrez (ed.), pp. 199-204. 2004. ACM Press, ISBN 1-58113-827-X. [ps] [bib]
Manuel Kauers. ZET User Manual. SFB F13. Technical report no. 2004-05, 2004. [ps] [bib]
P.J. Larcombe, A. Riese, B. Zimmermann. Computer Proofs of Matrix Product Identities. J. Algebra Appl. 3, pp. 105-109. 2004. ISSN 0219-4988. [pdf] [bib]
G. E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis XI: Hexagonal Plane Partitions. J. Kepler University Linz. Technical report no. 2004-4, March 2004. SFB-Report. [pdf] [bib]
G. E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis X: Plane Partitions with Diagonals.. Southeast Asian Journal Mathematics and Mathematical Sciences 3, pp. 3-14. 2004. ISSN 0972-7752. [pdf] [bib]
C. Schneider. Symbolic Summation with Single-Nested Sum Extensions (Extended Version). J. Kepler University, Linz. Technical report no. 2004-7, 2004. Published in Proc. ISSAC'04. SFB-Report. [pdf] [ps] [bib]
C. Schneider. Symbolic Summation with Single-Nested Sum Extensions. In: Proc. ISSAC'04, J. Gutierrez (ed.), pp. 282-289. 2004. ACM Press, ISBN 1-58113-827-X. [pdf] [ps] [bib]
C. Schneider. The summation package Sigma: Underlying principles and a rhombus tiling application. Discrete Math. Theor. Comput. Sci. 6(2), pp. 365-386. 2004. ISSN 1365-8050. [url] [pdf] [ps] [bib]
G.E. Andrews, P. Paule, C. Schneider. Plane Partition VI: Stembridge's TSPP Theorem -- A detailed algorithmic proof. Technical report no. 04-08 in RISC Report Series, University of Linz, Austria. May 2004. [ps] [pdf] [bib]
C. Schneider. A Collection of Denominator Bounds to Solve Parameterized Linear Difference Equations in ${\Pi}{\Sigma}$-Extensions. An. Univ. Timisoara Ser. Mat.-Inform. 42(2), pp. 163-179. 2004. ISSN 1224-970x. Extended version of Proc. SYNASC'04; preliminary version online. [pdf] [ps] [bib]
Manuel Kauers. Computing Limits of Sequences. 2003. Poster presentation at ISSAC 2003. [ps] [ps] [bib]
P. Paule, V. Strehl. Definite Summation and Hypergeometric Identities. In: Computer Algebra Handbook: Foundations, Applications, Systems, J. Grabmeier, E. Kaltofen, V. Weispfenning (ed.), pp. 91-93. 2003. Springer, ISBN: 3-540-65466-6. [bib]
P. Paule, O. Scherzer, A. Schoisswohl. Wavelets with Scale Dependent Properties. In: Symbolic and Numerical Scientific Computation, F. Winkler and U. Langer (ed.), Lecture Notes in Comput. Sci. 2630, pp. 255-265. 2003. Springer, ISBN: 0-89871-541-5. [ps] [bib]
P. Paule, H. Prodinger. Fountains, Histograms, and $q$-Identities. Discrete Math. Theor. Comput. Sci. 6, pp. 101-106. 2003. ISSN 1365-8050. [ps] [bib]
A. Riese. qMultiSum -- A Package for Proving q-Hypergeometric Multiple Summation Identities. J. Symbolic Comput. 35, pp. 349-376. 2003. ISSN 0747-7171. [pdf] [bib]
A. Riese. Computer Algebra Algorithms for Symbolic Summation. June 2003. Poster presentation at International Workshop on Numerical and Symbolic Scientific Computing, Strobl, Austria. [bib]
P. Paule, C. Schneider. Computer proofs of a new family of harmonic number identities. Adv. in Appl. Math. 31(2), pp. 359-378. 2003. ISSN 0196-8858. Preliminary version online. [ps] [pdf] [bib]
Burkhard Zimmermann. A Sister-Celine-type algorithm for definite summation and integration. August 2003. Poster presentation at ISSAC 2003. [bib]
A. Berkovich, A. Riese. A Computer Proof of a Polynomial Identity Implying a Partition Theorem of Göllnitz. Adv. in Appl. Math. 28, pp. 1-16. 2002. ISSN 0196-8858. [pdf] [bib]
F. Caruso. Polynomial Arithmetic and Linear Systems in Symbolic Summation. RISC Linz. PhD Thesis. 2002. [bib]
S. Gerhold. Uncoupling Systems of Linear Ore Operator Equations. RISC, J. Kepler University Linz. Diploma Thesis. 2 2002. [ps] [ps] [bib]
P. Paule. Actions of Finite Groups. In: The Concise Handbook of Algebra, A.V. Mikhalev, G.F. Pilz (ed.), pp. 119-123. 2002. Kluwer, ISBN 0-7923-7072-4. [bib]
I. Gutman, P. Paule. The Variance of the Vertex Degrees of Randomly Generated Graphs. Publ. Fac. Electr. Engrg. Ser. Mat. 13, pp. 30-35. 2002. ISSN 0354-124X. [bib]
R. Lyons, P. Paule, A. Riese. A Computer Proof of a Series Evaluation in Terms of Harmonic Numbers. Appl. Algebra Engrg. Comm. Comput. 13, pp. 327-333. 2002. ISSN 0938-1279. [pdf] [bib]
C. Schneider. How one can play with sums. In: Proceedings of the 8th Rhine Workshop on Computer Algebra, H. Kredel, W. Seiler (ed.), pp. 73-83. 2002. Mannheim, Germany, -. Preliminary version online. [ps] [pdf] [bib]
A. Berkovich, P. Paule. Variants of the Andrews-Gordon Identities. Ramanujan J. 5, pp. 391-404. 2001. ISSN 1382-4090. [pdf] [bib]
A. Berkovich, P. Paule. Lattice Paths, $q$-Multinomials and Two Variants of the Andrews-Gordon Identities. Ramanujan J. 5, pp. 409-424. 2001. ISSN 1382-4090. [pdf] [bib]
G.E. Andrews, A. Knopfmacher, P. Paule, H. Prodinger. $q$-Engel Series Expansions and Slater's Identities. Quaestiones Math. 24, pp. 403-416. 2001. ISSN 0379-9468. [pdf] [bib]
G.E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis III: The Omega Package. European J. Combin. 22, pp. 887-904. 2001. ISSN 0195-6698. [pdf] [bib]
G.E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis VI: A New Reduction Algorithm. Ann. Comb. 5, pp. 251-270. 2001. ISSN 0218-0006. [pdf] [bib]
G.E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis VII: Constrained Compositions. In: q-Series with Applications to Combinatorics, Number Theory, and Physics, B.C. Berndt and K. Ono (ed.), Contemp. Math. 291, pp. 11-27. 2001. Amer. Math. Soc., ISBN 0-8218-2746-4. [pdf] [bib]
G.E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis VIII: Plane Partition Diamonds. Adv. in Appl. Math. 27, pp. 231-242. 2001. ISSN 0196-8858. [pdf] [bib]
G.E. Andrews, P. Paule, A. Riese. MacMahon's Partition Analysis IX: k-Gon Partitions. Bull. Austral. Math. Soc. 64, pp. 321-329. 2001. ISSN 0004-9727. [pdf] [bib]
G.E. Andrews, P. Paule, A. Riese, V. Strehl. MacMahon's Partition Analysis V: Bijections, Recursions, and Magic Squares. In: Algebraic Combinatorics and Applications, A. Betten and others (ed.), pp. 1-39. 2001. Springer, ISBN 3-5404-1110-0. [pdf] [bib]
A. Riese. Fine-Tuning Zeilberger's Algorithm - The Methods of Automatic Filtering and Creative Substituting. In: Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, F.G. Garvan and M.E.H. Ismail (ed.), Developments in Mathematics 4, pp. 243-254. 2001. Kluwer, ISBN 1-4020-0101-0. [pdf] [bib]
C. Schneider. Symbolic Summation in Difference Fields. RISC, J. Kepler University Linz. PhD Thesis. May 2001. (published as Technical report no. 01-17 in RISC Report Series.). [ps] [pdf] [bib]
C. Weixlbaumer. Solutions of Difference Equations With Polynomial Coefficients. RISC, J. Kepler University Linz. Diploma Thesis. 2001. [pdf] [bib]
F. Chyzak, P. Paule, O. Scherzer, A. Schoisswohl, B. Zimmermann. The construction of orthonormal wavelets using symbolic methods and a matrix analytical approach for wavelets on the interval. Experiment. Math. 10, pp. 67-86. 2001. ISSN 1058-6458. [pdf] [bib]
G.E. Andrews, A. Knopfmacher, P. Paule, B. Zimmermann. Engel Expansions of $q$-Series by Computer Algebra. In: Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, F.G. Garvan and M.E.H. Ismail (ed.), Developments in Mathematics 4, pp. 33-57. 2001. Kluwer, ISBN: 1402001010. [pdf] [bib]
G.E. Andrews, A. Knopfmacher, P. Paule. An infinite family of Engel expansions of Rogers-Ramanujan type. Adv. in Appl. Math. 25, pp. 2-11. 2000. ISSN 0196-8858. [pdf] [bib]
P. Paule. Algorithmic Problem Solving. In: Encyclopedia of Computer Science, A. Ralston, E.D. Reilly, D. Hemmendinger (ed.), pp. 38-40. 2000. Nature Publishing Group, London, ISBN: 1850328005. [bib]
C. Schneider. An Implementation of {K}arr's Summation Algorithm in Mathematica. Sem. Lothar. Combin. S43b, pp. 1-10. 2000. ISSN 1286-4889. [url] [pdf] [ps] [bib]
Burkhard Zimmermann. Difference Forms and Hypergeometric Sums. Technical report no. 00-02 in RISC Report Series, University of Linz, Austria. February 2000. Master Thesis. [ps] [bib]
F. Caruso. A Macsyma Implementation of Zeilberger's Fast Algorithm. In: Sém. Lothar. Combin. S43c, V. Strehl (ed.), pp. 1-8. 1999. ISSN 1286-4889. [pdf] [ps] [ps] [bib]
G.E. Andrews, P. Paule. MacMahon's Partition Analysis IV: Hypergeometric Multisums. Sém. Lothar. Combin. B42i, pp. 1-24. 1999. electronic journal. [pdf] [bib]
F. Chyzak, I. Gutman, P. Paule. Predicting the number of hexagonal systems with 24 and 25 hexagons. Communications in Mathematical and Computer Chemistry 40, pp. 139-151. 1999. ISSN: 0340-6253. [pdf] [bib]
P. Hjorth, P. Lisonek, S. Markvorsen, C. Thomassen. Finite metric spaces of strictly negative type. Linear Algebra Appl. 270, pp. 255-273. 1998. ISSN 0024-3795. [bib]
J.M. Borwein, D.M. Bradley, D.J. Broadhurst, P. Lisonek. Combinatorial aspects of multiple zeta values. Electron. J. Combin. 5, pp. 1-12. 1998. ISSN 1077-8926. [bib]
S.A. Abramov, P. Paule, M. Petkovsek. $q$-Hypergeometric solutions of $q$-difference equations. Discrete Math. 180, pp. 3-22. 1998. ISSN 0012-365X. [pdf] [bib]
P. Lisonek. New maximal two-distance sets. J. Combin. Theory Ser. A 77, pp. 318-338. 1997. ISSN 0097-3165. [bib]
J.M. Borwein, P. Lisonek, J.A. Macdonald. Arithmetic-geometric means revisited. The Maple Technical Newsletter 4, pp. 20-27. 1997. ISSN 1061-5733. [bib]
I. Nemes, P. Paule. A Canonical Form Guide to Symbolic Summation. In: Advances in the Design of Symbolic Computation Systems, A. Miola, M. Temperini (ed.), Texts Monogr. Symbol. Comput. , pp. 84-110. 1997. Springer, Wien-New York, ISBN 3211828443. [bib]
P. Paule, A. Riese. A Mathematica q-Analogue of Zeilberger's Algorithm Based on an Algebraically Motivated Approach to q-Hypergeometric Telescoping. In: Special Functions, q-Series and Related Topics, M.E.H. Ismail and M. Rahman (ed.), Fields Inst. Commun. 14, pp. 179-210. 1997. Amer. Math. Soc., ISBN 0-8218-0524-X. [pdf] [bib]
A. Riese. Contributions to Symbolic q-Hypergeometric Summation. RISC, J. Kepler University Linz. PhD Thesis. 1997. [pdf] [bib]
M. Rosenkranz. Lagrange Inversion. RISC, J. Kepler University Linz. Diploma Thesis. 1997. [pdf] [ps] [ps] [bib]
C. Schneider. Implementierung von Automaten-Algorithmen mit Hilfe von binären Entscheidungsdiagrammen. Lehrstuhl für Künstliche Intelligenz (Informatik VIII), Friedrich Alexander Universität Erlangen-Nürnberg. Diploma Thesis. 1997. (Engl. translation: Implementation of Algorithms for Automatons with Binary Decision Diagrams - BDD). Diploma Thesis. [ps] [pdf] [bib]
K. Wegschaider. Computer Generated Proofs of Binomial Multi-Sum Identities. RISC, J. Kepler University. Diploma Thesis. May 1997. [ps] [bib]
C. Mallinger. Algorithmic Manipulations and Transformations of Univariate Holonomic Functions and Sequences. RISC, J. Kepler University. Diploma Thesis. August 1996. [ps] [pdf] [bib]
P. Paule. A Classical Hypergeometric Proof of an Important Transformation Formula Found by J.-B. Baillon and R.E. Bruck. In: Theory and Applications of Nonlinear Operators of Accretive and Monotype Type, A. G. Kartsatos (ed.), Lecture Notes in Pure and Appl. Math. 178, pp. 241-242. 1996. Marcel Dekker, ISBN 0824797213. [pdf] [bib]
P. Paule. A Proof of a Conjecture of Knuth. Experiment. Math. 5, pp. 83-89. 1996. ISSN 1058-6458. [pdf] [bib]
A. Riese. A Generalization of Gosper's Algorithm to Bibasic Hypergeometric Summation. Electron. J. Combin. 3(#R19), pp. 1-16. 1996. ISSN 1077-8926. [pdf] [bib]
P. Lisonek. Denumerants and their approximations. J. Combin. Math. Combin. Comput. 18, pp. 225-232. 1995. ISSN 0835-3026. [bib]
P. Lisonek. Local and global majorities revisited. Discrete Math. 146, pp. 153-158. 1995. ISSN 0012-365X. [bib]
P. Lisonek. Closed forms for the number of polygon dissections. J. Symbolic Comput. 20, pp. 595-601. 1995. ISSN 0747-7171. [bib]
I. Nemes, M. Petkovsek. RComp: A Mathematica Package for Computing with Recursive Sequences. J. Symbolic Comput. 20, pp. 745-753. 1995. ISSN 0747-7171. [bib]
P. Paule. Greatest Factorial Factorization and Symbolic Summation. J. Symbolic Comput. 20, pp. 235-268. 1995. ISSN 0747-7171. [pdf] [bib]
P. Paule, V. Strehl. Symbolic Summation - Some Recent Developments. In: Computer Algebra in Science and Engineering - Algorithms, Systems, and Applications, J. Fleischer et al. (ed.), pp. 138-162. 1995. World Scientific, Singapore, ISBN 981-02-2319-6. [pdf] [bib]
R. Pirastu. Algorithms for Indefinite Summation of Rational Functions in Maple. The Maple Technical Newsletter 2(1), pp. 1-12. 1995. ISSN 1061-5733. [ps] [pdf] [bib]
A. Riese. A Mathematica q-Analogue of Zeilberger's Algorithm for Proving q-Hypergeometric Identities. RISC, J. Kepler University Linz. Diploma Thesis. 1995. [pdf] [bib]
P. Paule, M. Schorn. A Mathematica Version of Zeilberger's Algorithm for Proving Binomial Coefficient Identities. J. Symbolic Comput. 20, pp. 673-698. 1995. ISSN 0747-7171. [pdf] [bib]
M. Schorn. Contributions to Symbolic Summation. RISC, J. Kepler University. Diploma Thesis. December 1995. [ps] [pdf] [bib]
P. Lisonek. Computer-assisted Studies in Algebraic Combinatorics. RISC, J. Kepler University Linz. PhD Thesis. 1994. [pdf] [ps] [bib]
P. J. Grabner, R. F. Tichy, I. Nemes, A. Petho. Generalized Zeckendorf Expansions. Appl. Math. Lett. 7, pp. 25-28. 1994. ISSN 0893-9659. [bib]
P. Paule. Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type. Electron. J. Combin. 1, pp. 1-9. 1994. ISSN 1077-8926. [pdf] [bib]
R. Folk, A. Kartashov, P. Lisonek, P. Paule. Symmetries in Neural Networks: A Linear Group Approach. J. Phys. A 26, pp. 3159-3164. 1993. ISSN 0305-4470. [bib]
P. Lisonek, P. Paule, V. Strehl. Improvement of the Degree Setting in Gosper's Algorithm. J. Symbolic Comput. 16, pp. 243-258. 1993. ISSN 0747-7171. [pdf] [bib]
G. E. Andrews, P. Paule. Some Questions Concerning Computer-Generated Proofs of a Binomial Double-Sum Identity. J. Symbolic Comput. 16, pp. 147-153. 1993. ISSN 0747-7171. [pdf] [bib]
R. Pirastu. Algorithmen zur Summation rationaler Funktionen. University of Erlangen-Nürnberg. Diploma Thesis. 1992. [pdf] [ps] [bib]
J. Bajer, P. Lisonek. Symbolic computation approach to nonlinear dynamics. J. Modern Opt. 38, pp. 719-729. 1991. ISSN 0950-0340. [bib]
I. Nemes. On the solution of a diophantine equation with sieve algorithm. In: Proceedings of the Colloquium on Computational Number Theory held at Kossuth Lajos University, Debrecen (Hungary), September 4-9, 1989, A. Pethö, M. E. Pohst, H. C. Williams, H. G. Zimmer (ed.), pp. 302-319. 1991. Walter de Gruyter, ISBN 3-11-012394-0. [bib]
P. Paule. A Note on Bailey's Lemma. J. Combin. Theory Ser. A 44, pp. 164-167. 1987. ISSN 0097-3165. [bib]
P. Paule. A Remark on a Lemma of Ingleton and Piff and the Construction of Bijections. Bayreuth. Math. Schr. 25, pp. 123-127. 1987. ISSN 0172-1062. [bib]
P. Paule. The Concept of Bailey Chains. Sém. Lothar. Combin. B18f, pp. 1-24. 1987. electronic journal. [pdf] [bib]
I. Nemes, A. Petho. Polynomial Values in Linear Recurrences, II. J. Number Theory 24, pp. 47-53. 1986. ISSN 0022-314X. [bib]
P. Paule. Über das Involutionsprinzip von Garsia und Milne. Bayreuth. Math. Schr. 21, pp. 295-319. 1986. ISSN 0172-1062. [bib]
P. Paule. On Identities of the Rogers-Ramanujan Type. J. Math. Anal. Appl. 107, pp. 255-284. 1985. ISSN 0022-247X. [bib]
P. Paule. Ein neuer Weg zur q-Lagrangeinversion. Bayreuth. Math. Schr. 18, pp. 1-37. 1985. ISSN 0172-1062. [bib]
P. Paule. Über die Inversionsstatistiken von MacMahon und Goulden-Jackson. Sém. Lothar. Combin. B13b, pp. 1-3. 1985. electronic journal. [pdf] [bib]