Lascoux polynomials are K-theoretic analogues of the key polynomials. They both have combinatorial formulas involving tableaux: reverse set-valued tableaux (RSVT) rule for Lascoux polynomials and reverse semistandard Young tableaux (RSSYT) rule for key polynomials. Furthermore, key polynomials have a simple algorithmic model in terms of Kohnert diagrams, which are in bijection with RSSYT. Ross and Yong introduced K-Kohnert diagrams, which are analogues of Kohnert diagrams. They conjectured a K-Kohnert diagram rule for Lascoux polynomials. We establish this conjecture by constructing a weight-preserving bijection between RSVT and K-Kohnert diagrams.
@article{10_37236_11434,
author = {Jianping Pan and Tianyi Yu},
title = {A bijection between {\(K\)-Kohnert} diagrams and reverse set-valued tableaux},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {4},
doi = {10.37236/11434},
zbl = {1533.05290},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11434/}
}
TY - JOUR
AU - Jianping Pan
AU - Tianyi Yu
TI - A bijection between \(K\)-Kohnert diagrams and reverse set-valued tableaux
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/11434/
DO - 10.37236/11434
ID - 10_37236_11434
ER -
%0 Journal Article
%A Jianping Pan
%A Tianyi Yu
%T A bijection between \(K\)-Kohnert diagrams and reverse set-valued tableaux
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/11434/
%R 10.37236/11434
%F 10_37236_11434
Jianping Pan; Tianyi Yu. A bijection between \(K\)-Kohnert diagrams and reverse set-valued tableaux. The electronic journal of combinatorics, Tome 30 (2023) no. 4. doi: 10.37236/11434
