English

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 2×n2\times n, and obtained a polynomial on the major index of these tableaux, which is a qq-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 2×n2 \times n. The resulting polynomials are both qq-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