Difference ascent sequences and related combinatorial structures

Ascent sequences were introduced by Bousquet-M & eacute;lou, Claesson, Dukes and Kitaev, and 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 B & eacute;nyi, 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 but not surjective. 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 difference d permutations and a class of factorial posets which we call difference d posets, both of which are shown 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. (c) 2025 Published by Elsevier Ltd.