Pattern avoidance in ascent sequences

TL;DR

This paper investigates pattern avoidance in ascent sequences, establishing combinatorial connections, analyzing growth rates, and exploring Wilf equivalence for patterns of length up to four.

Contribution

It provides new results on pattern avoidance in ascent sequences, including bijections with other combinatorial objects and conjectures on their properties.

Findings

Results for patterns of length up to 4

Connections with set partitions and other structures

Conjectures on growth rates and Wilf equivalence

Abstract

Ascent sequences are sequences of nonnegative integers with restrictions on the size of each letter, depending on the number of ascents preceding it in the sequence. Ascent sequences have recently been related to (2+2)-free posets and various other combinatorial structures. We study pattern avoidance in ascent sequences, giving several results for patterns of lengths up to 4, for Wilf equivalence and for growth rates. We establish bijective connections between pattern avoiding ascent sequences and various other combinatorial objects, in particular with set partitions. We also make a number of conjectures related to all of these aspects.