Séminaire Lotharingien de Combinatoire, 89B.30 (2023), 12 pp.
Andrei Asinowski, Cyril Banderier and
Sarah J. Selkirk
From Kreweras to Gessel: A Walk through Patterns in the Quarter Plane
Abstract.
We initiate a study of pattern avoidance in quarter-plane lattice walks.
First we demonstrate surprising links between Kreweras excursions (avoiding a pattern of length 2)
and some famous lattice walk models, such as Gessel, Gouyou-Beauchamps, and P\'olya excursions.
Next we explore the nature (algebraic, hypergeometric, D-finite) of the corresponding generating functions.
In particular, we show that pattern avoidance does not necessarily preserve algebraicity or D-finiteness.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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