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Chapitre D'ouvrage Année : 2021

On the Kernel Curves Associated with Walks in the Quarter Plane

Résumé

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).
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Dates et versions

hal-03513338 , version 1 (05-01-2022)

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Thomas Dreyfus, Charlotte Hardouin, Julien Roques, Michael F Singer. On the Kernel Curves Associated with Walks in the Quarter Plane. Alin Bostan; Kilian Raschel. Transcendence in Algebra, Combinatorics, Geometry and Number Theory. TRANS19 – Transient Transcendence in Transylvania, Brașov, Romania, May 13–17, 2019, Revised and Extended Contributions, 373, Springer International Publishing, pp.61-89, 2021, Springer Proceedings in Mathematics & Statistics, 978-3-030-84303-8. ⟨10.1007/978-3-030-84304-5_3⟩. ⟨hal-03513338⟩
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