We prove that a family of average weights for oscillating tableaux are polynomials in two variables, namely, the length of the oscillating tableau and the size of the ending partition, which generalizes a result of Hopkins and Zhang. Several explicit and asymptotic formulas for the average weights are also derived. The main idea in this paper is to translate the study of certain average weights for oscillating tableaux to the study of an operator $\Psi$ from the set of real coefficient polynomials with two parameters to itself.
@article{10_37236_7722,
author = {Guo-Niu Han and Huan Xiong},
title = {Polynomiality of certain average weights for oscillating tableaux},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {4},
doi = {10.37236/7722},
zbl = {1398.05028},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7722/}
}
TY - JOUR
AU - Guo-Niu Han
AU - Huan Xiong
TI - Polynomiality of certain average weights for oscillating tableaux
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/7722/
DO - 10.37236/7722
ID - 10_37236_7722
ER -
%0 Journal Article
%A Guo-Niu Han
%A Huan Xiong
%T Polynomiality of certain average weights for oscillating tableaux
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/7722/
%R 10.37236/7722
%F 10_37236_7722
Guo-Niu Han; Huan Xiong. Polynomiality of certain average weights for oscillating tableaux. The electronic journal of combinatorics, Tome 25 (2018) no. 4. doi: 10.37236/7722
