Séminaire Lotharingien de Combinatoire, 84B.95 (2020), 12 pp.

Andrei Asinowski, Cyril Banderier and Valerie Roitner

Generating Functions for Lattice Paths with Several Forbidden Patterns

Abstract. This work studies directed lattice paths on Z2, constrained to avoid a set of given patterns. We give the corresponding generating functions, for walks, meanders (walks additionally constrained to be above the x-axis), and excursions (meanders constrained to end on the x-axis). Our method relies on a vectorial generalization of the classical kernel method, and on a matricial generalization of the autocorrelation polynomial. We apply our approach on more than 512 different models, thus unifying/extending many previous works.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

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