Refining the bijections among ascent sequences, (2+2)-free posets, integer matrices and pattern-avoiding permutations
Abstract
The combined work of Bousquet-M\'elou, Claesson, Dukes, Jel\'inek, 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.
Cite
@article{arxiv.1807.11505,
title = {Refining the bijections among ascent sequences, (2+2)-free posets, integer matrices and pattern-avoiding permutations},
author = {Mark Dukes and Peter R. W. McNamara},
journal= {arXiv preprint arXiv:1807.11505},
year = {2019}
}
Comments
24 pages, 4 figures. To appear in Journal of Combinatorial Theory, Series A