Automatic Classification of Restricted Lattice Walks

Alin Bostan; Manuel Kauers

doi:10.46298/dmtcs.2724

Alin Bostan ; Manuel Kauers - Automatic Classification of Restricted Lattice Walks

dmtcs:2724 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2724

Automatic Classification of Restricted Lattice WalksConference paper

Authors: Alin Bostan ¹; Manuel Kauers ²

1 Algorithms
2 Research Institute for Symbolic Computation

We propose an $\textit{experimental mathematics approach}$ leading to the computer-driven $\textit{discovery}$ of various conjectures about structural properties of generating functions coming from enumeration of restricted lattice walks in 2D and in 3D.

https://doi.org/10.46298/dmtcs.2724

Source: HAL:hal-00780428v1

Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)

Section: Proceedings

Published on: January 1, 2009

Imported on: January 31, 2017

Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] Automated guessing, lattice paths, generating functions, computer algebra, enumeration

Funding:

Source : OpenAIRE Graph

Symbolic Integration and Special Functions; Code: P 20162
Summation//Integration and Algebraic Relations; Code: P 19462

Bibliographic References

24 Documents citing this article

Alexander Kroitor;Stephen Melczer, 2024, Completing the Asymptotic Classification of Mostly Symmetric Short Step Walks in an Orthant, Annals of Combinatorics, 29, 2, pp. 575-599, 10.1007/s00026-024-00739-6.

Benjamin Buckley;Marni Mishna, 2024, Uniform Sampling and Visualization of 3D Reluctant Walks, Electronic Proceedings in Theoretical Computer Science, 403, pp. 66-72, 10.4204/eptcs.403.16, https://doi.org/10.4204/eptcs.403.16.

Manuel Kauers, 2023, Summation and Integration, Algorithms and computation in mathematics, pp. 393-509, 10.1007/978-3-031-34652-1_5.

Manuel Kauers, 2023, Operators, Algorithms and computation in mathematics, pp. 287-391, 10.1007/978-3-031-34652-1_4.

Manuel Kauers, 2023, Background and Fundamental Concepts, Algorithms and computation in mathematics, pp. 1-80, 10.1007/978-3-031-34652-1_1.

Manuel Kauers, 2023, The Recurrence Case in One Variable, Algorithms and computation in mathematics, pp. 81-183, 10.1007/978-3-031-34652-1_2.

Manuel Kauers, 2023, The Differential Case in One Variable, Algorithms and computation in mathematics, pp. 185-286, 10.1007/978-3-031-34652-1_3.

Alin Bostan;Frédéric Chyzak;Hadrien Notarantonio;Mohab Safey El Din, 2022, Algorithms for Discrete Differential Equations of Order 1, Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, pp. 101-110, 10.1145/3476446.3535471.

Alin Bostan, 2021, Computer Algebra in the Service of Enumerative Combinatorics, 172, pp. 1-8, 10.1145/3452143.3465507, https://hal.science/hal-03427873.

Alin Bostan;Andrew Elvey Price;Anthony John Guttmann;Jean-Marie Maillard, 2020, Stieltjes Moment Sequences for Pattern-Avoiding Permutations, The Electronic Journal of Combinatorics, 27, 4, 10.37236/9402, https://doi.org/10.37236/9402.

Stephen Melczer, 2020, Application: Lattice Paths, Revisited, Texts & monographs in symbolic computation/Texts and monographs in symbolic computation, pp. 387-405, 10.1007/978-3-030-67080-1_10.

Stephen Melczer, 2020, Application: LatticeWalks and Smooth ACSV, Texts & monographs in symbolic computation/Texts and monographs in symbolic computation, pp. 247-262, 10.1007/978-3-030-67080-1_6.

Stephen Melczer, 2020, Introduction, Texts & monographs in symbolic computation/Texts and monographs in symbolic computation, pp. 1-18, 10.1007/978-3-030-67080-1_1.

Stephen Melczer, 2020, Lattice Path Enumeration, The Kernel Method, and Diagonals, Texts & monographs in symbolic computation/Texts and monographs in symbolic computation, pp. 143-181, 10.1007/978-3-030-67080-1_4.

Alin Bostan;Mireille Bousquet-Mélou;Manuel Kauers;Stephen Melczer, 2016, On 3-Dimensional Lattice Walks Confined to the Positive Octant, arXiv (Cornell University), 20, 4, pp. 661-704, 10.1007/s00026-016-0328-7, http://arxiv.org/abs/1409.3669.

Alin Bostan;Xavier Caruso;Éric Schost, 2015, A Fast Algorithm for Computing the P-curvature, arXiv (Cornell University), pp. 69-76, 10.1145/2755996.2756674, http://arxiv.org/abs/1506.05645.

Stephen Melczer;Marni Mishna, 2015, Asymptotic Lattice Path Enumeration Using Diagonals, Algorithmica, 75, 4, pp. 782-811, 10.1007/s00453-015-0063-1.

Alin Bostan;Xavier Caruso;Éric Schost, 2014, A fast algorithm for computing the characteristic polynomial of the p-curvature, arXiv (Cornell University), pp. 59-66, 10.1145/2608628.2608650, http://arxiv.org/abs/1405.5341.

Stephen Melczer;Marni Mishna, 2014, Singularity Analysis Via the Iterated Kernel Method, arXiv (Cornell University), 23, 5, pp. 861-888, 10.1017/s0963548314000145, http://arxiv.org/abs/1303.3236.

IVO J. B. F. ADAN;JOHAN S. H. van LEEUWAARDEN;KILIAN RASCHEL;IVO J. B. F. ADAN;JOHAN S. H. van LEEUWAARDEN;et al., 2013, The Compensation Approach for Walks With Small Steps in the Quarter Plane, arXiv (Cornell University), 22, 2, pp. 161-183, 10.1017/s0963548312000594, http://arxiv.org/abs/1101.0804.

Guy Fayolle;Kilian Raschel, 2012, Some exact asymptotics in the counting of walks in the quarter plane, Discrete Mathematics & Theoretical Computer Science, DMTCS Proceedings vol. AQ,..., Proceedings, 10.46298/dmtcs.2988, https://doi.org/10.46298/dmtcs.2988.

Waldemar Hebisch;Martin Rubey, 2011, Extended rate, more GFUN, Journal of Symbolic Computation, 46, 8, pp. 889-903, 10.1016/j.jsc.2011.01.004.

Alin Bostan;Éric Schost, 2009, Fast algorithms for differential equations in positive characteristic, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, pp. 47-54, 10.1145/1576702.1576712.

Peter Paule;Bruno Buchberger;Lena Kartashova;Manuel Kauers;Carsten Schneider;et al., 2009, Algorithms in Symbolic Computation, Hagenberg Research, pp. 5-62, 10.1007/978-3-642-02127-5_2.

Sources : OpenCitations, OpenAlex & Crossref

Share and export

Consultation statistics

This page has been seen 477 times.

This article's PDF has been downloaded 384 times.