Recently O. Pechenik studied the cyclic sieving of increasing tableaux of shape $2\times n$, and obtained a polynomial on the major index of these tableaux, which is a $q$-analogue of refined small Schröder numbers. We define row-increasing tableaux and study the major index and amajor index of row-increasing tableaux of shape $2 \times n$. The resulting polynomials are both $q$-analogues of refined large Schröder numbers. For both results we give bijective proofs.
@article{10_37236_8087,
author = {Rosena R.X. Du and Xiaojie Fan and Yue Zhao},
title = {Enumeration on row-increasing tableaux of shape \(2 \times n\)},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {1},
doi = {10.37236/8087},
zbl = {1409.05017},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8087/}
}
TY - JOUR
AU - Rosena R.X. Du
AU - Xiaojie Fan
AU - Yue Zhao
TI - Enumeration on row-increasing tableaux of shape \(2 \times n\)
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/8087/
DO - 10.37236/8087
ID - 10_37236_8087
ER -
%0 Journal Article
%A Rosena R.X. Du
%A Xiaojie Fan
%A Yue Zhao
%T Enumeration on row-increasing tableaux of shape \(2 \times n\)
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/8087/
%R 10.37236/8087
%F 10_37236_8087
Rosena R.X. Du; Xiaojie Fan; Yue Zhao. Enumeration on row-increasing tableaux of shape \(2 \times n\). The electronic journal of combinatorics, Tome 26 (2019) no. 1. doi: 10.37236/8087
