On the Kernel curves associated with walks in the quarter plane
Combinatorics
2024-10-22 v2
Abstract
The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel polynomial, and using properties of the curve, the kernel curve, this defines. In the present paper, we investigate the basic properties of the kernel curve (irreducibility, singularities, genus, uniformization, etc).
Keywords
Cite
@article{arxiv.2004.01035,
title = {On the Kernel curves associated with walks in the quarter plane},
author = {Thomas Dreyfus and Charlotte Hardouin and Julien Roques and Michael F. Singer},
journal= {arXiv preprint arXiv:2004.01035},
year = {2024}
}
Comments
This paper is mainly the old Section 4 of the paper: Walks in the quarter plane, genus zero case. arXiv admin note: substantial text overlap with arXiv:1710.02848