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Article Dans Une Revue Annals of Combinatorics Année : 2021

On the Nature of Four Models of Symmetric Walks Avoiding a Quadrant

Amélie Trotignon
  • Fonction : Auteur

Résumé

We study the nature of the generating series of some models of walks with small steps in the three quarter plane. More precisely, we restrict ourselves to the situation where the group is infinite, the kernel has genus one, and the step set is diagonally symmetric (i.e., with no steps in anti-diagonal directions). In that situation, after a transformation of the plane, we derive a quadrant-like functional equation. Among the four models of walks, we obtain, using difference Galois theory, that three of them have a differentially transcendental generating series, and one has a differentially algebraic generating series.
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Dates et versions

hal-03357218 , version 1 (28-09-2021)

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Thomas Dreyfus, Amélie Trotignon. On the Nature of Four Models of Symmetric Walks Avoiding a Quadrant. Annals of Combinatorics, 2021, 25 (3), pp.617-644. ⟨10.1007/s00026-021-00541-8⟩. ⟨hal-03357218⟩
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