This paper extends Lewis's bijection (J. Combin. Theorey Ser. A 118, 2011) to a bijection between a more general class $\mathcal{L}(n,k,I)$ of permutations and the set of standard Young tableaux of shape $\langle (k+1)^n\rangle$, so the cardinality\[|\mathcal{L}(n,k,I)|=f^{\langle (k+1)^n\rangle},\]is independent of the choice of $I\subseteq [n]$. As a consequence, we obtain some new combinatorial realizations and identities on Catalan numbers. In the end, we raise a problem on finding a bijection between $\mathcal{L}(n,k,I)$ and $\mathcal{L}(n,k,I')$ for distinct $I$ and $I'$.
@article{10_37236_6427,
author = {Zhousheng Mei and Suijie Wang},
title = {Pattern avoidance and {Young} tableaux},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {1},
doi = {10.37236/6427},
zbl = {1355.05270},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6427/}
}
TY - JOUR
AU - Zhousheng Mei
AU - Suijie Wang
TI - Pattern avoidance and Young tableaux
JO - The electronic journal of combinatorics
PY - 2017
VL - 24
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6427/
DO - 10.37236/6427
ID - 10_37236_6427
ER -
%0 Journal Article
%A Zhousheng Mei
%A Suijie Wang
%T Pattern avoidance and Young tableaux
%J The electronic journal of combinatorics
%D 2017
%V 24
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6427/
%R 10.37236/6427
%F 10_37236_6427
Zhousheng Mei; Suijie Wang. Pattern avoidance and Young tableaux. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/6427
