Enumeration on row-increasing tableaux of shape $2 \times n$
Combinatorics
2019-03-19 v4
Abstract
Recently O. Pechenik studied the cyclic sieving of increasing tableaux of shape , and obtained a polynomial on the major index of these tableaux, which is a -analogue of refined small Schr\"{o}der numbers. We define row-increasing tableaux and study the major index and amajor index of row-increasing tableaux of shape . The resulting polynomials are both -analogues of refined large Schr\"{o}der numbers. For both results we give bijective proofs.
Keywords
Cite
@article{arxiv.1803.01590,
title = {Enumeration on row-increasing tableaux of shape $2 \times n$},
author = {Rosena R. X. Du and Xiaojie Fan and Yue Zhao},
journal= {arXiv preprint arXiv:1803.01590},
year = {2019}
}
Comments
We corrected some typos and modified the proof of Theorem 2.7