Increasing tableaux and Narayana numbers
Combinatorics
2018-08-20 v2
Abstract
We give a counting formula for the set of rectangular increasing tableaux in terms of generalized Narayana numbers. We define small -Schr\"oder paths and give a bijection between the set of increasing rectangular tableaux and small -Schr\"oder paths, generalizing a result of Pechenik [3]. Using -jeu de taquin promotion, which was defined by Thomas and Yong [10], we give a cyclic sieving phenomenon for the set of increasing hook tableaux.
Cite
@article{arxiv.1409.2841,
title = {Increasing tableaux and Narayana numbers},
author = {Timothy Pressey and Anna Stokke and Terry Visentin},
journal= {arXiv preprint arXiv:1409.2841},
year = {2018}
}