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 WalksArticle

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

Funding:

Source : OpenAIRE Graph

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

Bibliographic References

20 Documents citing this article

Alin Bostan;Frédéric Chyzak;Hadrien Notarantonio;Mohab Safey El Din, Algorithms for Discrete Differential Equations of Order 1, pp. 101-110, 2022, Villeneuve-d'Ascq France, 10.1145/3476446.3535471, https://hal.inria.fr/hal-03673294.

Manuel Kauers;Christoph Koutschan, arXiv (Cornell University), Guessing with Little Data, pp. 83-90, 2022, Villeneuve-d'Ascq France, 10.1145/3476446.3535486, http://arxiv.org/abs/2202.07966.

Alin Bostan, Computer Algebra in the Service of Enumerative Combinatorics, pp. 1-8, 2021, Virtual Event Russian Federation, 10.1145/3452143.3465507, https://hal.archives-ouvertes.fr/hal-03427873/file/issac21-hal.pdf.

Alin Bostan;Mireille Bousquet-Mélou;Stephen Melczer, 2021, Counting walks with large steps in an orthant, Journal of the European Mathematical Society, 23, 7, pp. 2221-2297, 10.4171/jems/1053, https://doi.org/10.4171/jems/1053.

Manfred Buchacher;Sophie Hofmanninger;Manuel Kauers, 2021, Walks with Small Steps in the 4D-Orthant, Annals of Combinatorics, 25, 1, pp. 153-166, 10.1007/s00026-020-00520-5, https://doi.org/10.1007/s00026-020-00520-5.

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

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

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

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

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.

Stephen Melczer;Marni Mishna, 2015, Asymptotic Lattice Path Enumeration Using Diagonals, arXiv (Cornell University), 75, 4, pp. 782-811, 10.1007/s00453-015-0063-1, https://arxiv.org/abs/1402.1230.

Alin Bostan;Xavier Caruso;Éric Schost, arXiv (Cornell University), A fast algorithm for computing the characteristic polynomial of the p-curvature, 276, pp. 59-66, 2014, Kobe Japan, 10.1145/2608628.2608650, http://arxiv.org/abs/1405.5341.

STEPHEN MELCZER;MARNI MISHNA, 2014, Singularity Analysis Via the Iterated Kernel Method, 23, 5, pp. 861-888, 10.1017/s0963548314000145, https://hal.inria.fr/hal-01229731.

IVO J. B. F. ADAN;JOHAN S. H. van LEEUWAARDEN;KILIAN RASCHEL, 2013, The Compensation Approach for Walks With Small Steps in the Quarter Plane, 22, 2, pp. 161-183, 10.1017/s0963548312000594, https://hal.science/hal-00551472.

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, https://doi.org/10.1016/j.jsc.2011.01.004.

Mireille Bousquet-Mélou;Marni Mishna, 2010, Walks with small steps in the quarter plane, Contemporary mathematics - American Mathematical Society, pp. 1-39, 10.1090/conm/520/10252, https://doi.org/10.1090/conm/520/10252.

Alin Bostan;Éric Schost, Fast algorithms for differential equations in positive characteristic, 97, pp. 47-54, 2009, Seoul Republic of Korea, 10.1145/1576702.1576712, https://hal.inria.fr/inria-00355818/file/BoSc09.pdf.

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

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