Séminaire Lotharingien de Combinatoire, 87B.10 (2023), 23 pp.

Thomas Dreyfus

Differential algebraic generating functions of walks in the quarter plane

Abstract. In the present paper we study the nature of the trivariate generating functions of weighted walks in the quarter plane. Combining the results of this paper to previous ones, we complete the proof of the following theorem. The series satisfies a nontrivial algebraic differential equation in one of its variables, if and only if it satisfies a nontrivial algebraic differential equation in each of its variables.

Received: October 12, 2021. Revised: December 20, 2022. Published: August 31, 2023.

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If you need to cite this article, here is a bibtex:

@article{Dreyfus23,
author = {Dreyfus, Thomas},
title = {Differential algebraic generating functions of walks in the quarter plane},
fjournal = {S{\'e}minaire Lotharingien de Combinatoire},
journal = {S{\'e}min. Lothar. Combin.},
issn={1286-4889},
volume = {87B},
number= {10},
pages = {1--23},
year = {2023},
language = {English},
doi={10.48550/arXiv.2104.05505},
}