Weak ascent sequences and related combinatorial structures. (February 2023)

• Record Type: Journal Article
• Authors: Bényi, Beáta; Claesson, Anders; Dukes, Mark
• Is Part Of: European journal of combinatorics. Volume 108(2023)
• Publication Date: 2023-02
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2022.103633
• Languages: English
• ISSNs: 0195-6698

Abstract

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.