Pipe dreams and bumpless pipe dreams for vexillary permutations are each known to be in bijection with certain semistandard tableaux via maps due to Lenart and Weigandt, respectively. Recently, Gao and Huang have defined a bijection between the former two sets. In this note we show for vexillary permutations that the Gao-Huang bijection preserves the associated tableaux, giving a new proof of Lenart's result. Our methods extend to give a recording tableau for any bumpless pipe dream.
@article{10_37236_11391,
author = {Adam Gregory and Zachary Hamaker},
title = {Lenart's bijection via bumpless pipe dreams},
journal = {The electronic journal of combinatorics},
year = {2023},
volume = {30},
number = {1},
doi = {10.37236/11391},
zbl = {1507.05100},
url = {http://geodesic.mathdoc.fr/articles/10.37236/11391/}
}
TY - JOUR
AU - Adam Gregory
AU - Zachary Hamaker
TI - Lenart's bijection via bumpless pipe dreams
JO - The electronic journal of combinatorics
PY - 2023
VL - 30
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/11391/
DO - 10.37236/11391
ID - 10_37236_11391
ER -
%0 Journal Article
%A Adam Gregory
%A Zachary Hamaker
%T Lenart's bijection via bumpless pipe dreams
%J The electronic journal of combinatorics
%D 2023
%V 30
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/11391/
%R 10.37236/11391
%F 10_37236_11391
Adam Gregory; Zachary Hamaker. Lenart's bijection via bumpless pipe dreams. The electronic journal of combinatorics, Tome 30 (2023) no. 1. doi: 10.37236/11391
