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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 **Z**^{2}, 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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