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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:167

Article

Dukes, Mark¹  McNamara, Peter R. W.² 

[1] Univ Coll Dublin, UCD Sch Math & Stat, Dublin 4, Ireland

[2] Bucknell Univ, Dept Math, Lewisburg, PA 17837 USA

关键词: Ascent sequence;    (2+2)-free poset;    Interval order;    Upper-diagonal matrix;    Pattern avoidance;    Series-parallel poset;   

DOI  :  10.1016/j.jcta.2019.05.007

来源: Elsevier

【 摘 要 】

The combined work of Bousquet-Melou, Claesson, Dukes, Jelinek, Kitaev, Kubitzke and Parviainen has resulted in nontrivial bijections among ascent sequences, (2+2)-free posets, upper-triangular integer matrices, and pattern-avoiding permutations. To probe the finer behaviour 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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free