Title

Refining the bijections among ascent sequences, (2+2)-free posets, integer matrices and pattern-avoiding permutations

Publication Date

11-2019

Description

The combined work of Bousquet-Mélou, Claesson, Dukes, Jelínek, Kitaev, Kubitzke and Parviainen has resulted in non-trivial bijections among ascent sequences, (2+2)-free posets, upper-triangular integer matrices, and pattern-avoiding permutations. To probe the finer behavior of these bijections, we study two types of restrictions on ascent sequences. These restrictions are motivated by our results that their images under the bijections are natural and combinatorially significant. In addition, for one restriction, we are able to determine the effect of poset duality on the corresponding ascent sequences, matrices and permutations, thereby answering a question of the first author and Parviainen in this case. The second restriction should appeal to Catalaniacs.

Journal

Journal of Combinatorial Theory (Series A)

Volume

167

First Page

403

Last Page

430

Department

Mathematics

DOI

https://doi.org/10.1016/j.jcta.2019.05.007

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