Lenart's bijection via bumpless pipe dreams
Combinatorics
2022-07-04 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2207.00523,
title = {Lenart's bijection via bumpless pipe dreams},
author = {Adam Gregory and Zachary Hamaker},
journal= {arXiv preprint arXiv:2207.00523},
year = {2022}
}
Comments
19 pages including 6 page appendix