Difference ascent sequences and related combinatorial structures

Ascent sequences were introduced by Bousquet-Mélou, Claesson, Dukes and Kitaev, which are in bijection with unlabeled \((2+2)\)-free posets, Fishburn matrices, permutations avoiding a bivincular pattern of length \(3\), and Stoimenow matchings. Analogous results for weak ascent sequences have been o...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2024-05
Main Authors: Zang, Yongchun, Zhou, Robin D P
Format: Article
Language:English
Subjects:
Combinatorial analysis
Permutations
Set theory
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Ascent sequences were introduced by Bousquet-Mélou, Claesson, Dukes and Kitaev, which are in bijection with unlabeled \((2+2)\)-free posets, Fishburn matrices, permutations avoiding a bivincular pattern of length \(3\), and Stoimenow matchings. Analogous results for weak ascent sequences have been obtained by Bényi, Claesson and Dukes. Recently, Dukes and Sagan introduced a more general class of sequences which are called \(d\)-ascent sequences. They showed that some maps from the weak case can be extended to bijections for general \(d\) while the extensions of others continue to be injective. The main objective of this paper is to restore these injections to bijections. To be specific, we introduce a class of permutations which we call them \(d\)-permutations and a class of factorial posets which we call them \(d\)-posets, both of which are showed to be in bijection with \(d\)-ascent sequences. Moreover, we also give a direct bijection between a class of matrices with a certain column restriction and Fishburn matrices. Our results give answers to several questions posed by Dukes and Sagan.
ISSN:2331-8422