Pattern Avoidance in Weak Ascent Sequences

Beáta Bényi, Toufik Mansour, José L. Ramírez

Published 2023-09-12Version 1

In this paper, we study the pattern avoidance in weak ascent sequences, giving some results for patterns of length 3. This is an analogous study to one given by Duncan and Steingr\'imsson for ascent sequences. More precisely, we provide systematically the generating functions for the number of weak ascent sequences avoiding the patterns $012, 021, 001, 102$, and $011$. We also establish bijective connections between pattern-avoiding weak ascent sequences and other combinatorial objects, such as compositions, upper triangular 01-matrices, and ordered trees. We leave as an open question the enumeration of the remaining cases of length 3.