Weak ascent sequences and related combinatorial structures
Combinatorics
2022-10-11 v2
Abstract
In this paper we introduce {\em weak ascent sequences}, a class of number sequences that properly contains ascent sequences. We show how these sequences uniquely encode each of the following objects: permutations avoiding a particular length-4 bivincular pattern; upper-triangular binary matrices that satisfy a column-adjacency rule; factorial posets that are weakly (3+1)-free. We also show how weak ascent sequences are related to a class of pattern avoiding inversion sequences that has been a topic of recent research by Auli and Elizalde. Finally, we consider the problem of enumerating these new sequences and give a closed form expression for the number of weak ascent sequences having a prescribed length and number of weak ascents.
Cite
@article{arxiv.2111.03159,
title = {Weak ascent sequences and related combinatorial structures},
author = {Beáta Bényi and Anders Claesson and Mark Dukes},
journal= {arXiv preprint arXiv:2111.03159},
year = {2022}
}