Pattern Avoidance in Weak Ascent Sequences

TL;DR

This paper investigates pattern avoidance in weak ascent sequences, providing generating functions for specific patterns and establishing bijections with various combinatorial structures.

Contribution

It systematically derives generating functions for pattern-avoiding weak ascent sequences and connects them to other combinatorial objects, extending prior ascent sequence studies.

Findings

Generated explicit formulas for avoiding patterns 001, 011, 012, 021, 102.

Established bijections with compositions, matrices, and trees.

Extended pattern avoidance analysis to weak ascent sequences.

Abstract

In this paper, we study 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 (2011) for ascent sequences. More precisely, we provide systematically the generating functions for the number of weak ascent sequences avoiding the patterns $001, 011, 012, 021$, and $102$. Additionally, we establish bijective connections between pattern-avoiding weak ascent sequences and other combinatorial objects, such as compositions, upper triangular 01-matrices, and plane trees.