In this manuscript we show that two partial orders defined on the set of standard Young tableaux of shape $\alpha$ are equivalent. In fact, we give two proofs for the equivalence of the box order and the dominance order for tableaux. Both are algorithmic. The first of these proofs emphasizes links to the Bruhat order for the symmetric group and the second provides a more straightforward construction of the cover relations. This work is motivated by the known result that the equivalence of the two combinatorial orders leads to a description of the geometry of the representation space of invariant subspaces of nilpotent linear operators.
@article{10_37236_5967,
author = {Justyna Kosakowska and Markus Schmidmeier and Hugh Thomas},
title = {Two partial orders for standard {Young} tableaux},
journal = {The electronic journal of combinatorics},
year = {2019},
volume = {26},
number = {3},
doi = {10.37236/5967},
zbl = {1427.05229},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5967/}
}
TY - JOUR
AU - Justyna Kosakowska
AU - Markus Schmidmeier
AU - Hugh Thomas
TI - Two partial orders for standard Young tableaux
JO - The electronic journal of combinatorics
PY - 2019
VL - 26
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/5967/
DO - 10.37236/5967
ID - 10_37236_5967
ER -
%0 Journal Article
%A Justyna Kosakowska
%A Markus Schmidmeier
%A Hugh Thomas
%T Two partial orders for standard Young tableaux
%J The electronic journal of combinatorics
%D 2019
%V 26
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/5967/
%R 10.37236/5967
%F 10_37236_5967
Justyna Kosakowska; Markus Schmidmeier; Hugh Thomas. Two partial orders for standard Young tableaux. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/5967
