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arXiv · 2111.03159

Weak ascent sequences and related combinatorial structures

Beáta Bényi·Anders Claesson·Mark Dukes
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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.

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Beáta Bényi, Anders Claesson, Mark Dukes. 2021-11-04. Weak ascent sequences and related combinatorial structures. https://arxiv.org/abs/2111.03159

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