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
Link to Published Version
https://www.sciencedirect.com/science/article/abs/pii/S0097316519300688
DOI
https://doi.org/10.1016/j.jcta.2019.05.007
Recommended Citation
Dukes, Mark and McNamara, Peter R. W.. "Refining the bijections among ascent sequences, (2+2)-free posets, integer matrices and pattern-avoiding permutations." (2019) : 403-430.
