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Conference Papers Year : 2021

Computer Algebra in the Service of Enumerative Combinatorics

Alin Bostan
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Abstract

Classifying lattice walks in restricted lattices is an important problem in enumerative combinatorics. Recently, computer algebra has been used to explore and to solve a number of difficult questions related to lattice walks. We give an overview of recent results on structural properties (e.g., algebraicity versus transcendence) and on explicit formulas for generating functions of walks with small steps in the quarter plane. In doing so, we emphasize the algorithmic nature of the methodology, especially two important paradigms: "guess-and-prove" and "creative telescoping".
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Dates and versions

hal-03427873 , version 1 (14-11-2021)

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Alin Bostan. Computer Algebra in the Service of Enumerative Combinatorics. International Symposium on Symbolic and Algebraic Computation (ISSAC), Jul 2021, Saint Petersburg, Russia. pp. 1-8, ⟨10.1145/3452143.3465507⟩. ⟨hal-03427873⟩
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