Weak Ascent Sequences and Related Combinatorial Structures
MTMT : 33556528
Date : 2023
Journal title : European Journal of Combinatorics
Journal volume : 108
Journal issue number : February
Pages : 103633
Document type : folyóiratcikk
Subject : Weak ascent sequence, (2+2)-free poset, Bivincular pattern, Pattern avoiding permutation, Enumeration, Természettudományok, Természettudományok/Matematika- és számítástudományok
Abstract :
In this paper we introduce 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.