Lattices properties of acyclic alternating pipe dreams
Combinatorics
2023-11-30 v2
Abstract
This paper proves some conjectures raised by N. Bergeron, N. Cartier, C. Ceballos, and V. Pilaud about acyclic facets of subword complexes of type A Coxeter groups. We use a representation of subword complex facets extending the pipe dreams defined N. Bergeron and S. Billey and prove that the strongly acyclic facets realize a lattice quotient of a weak order interval. We also give a sufficient condition so that all acyclic facets are strongly acyclic.
Keywords
Cite
@article{arxiv.2311.10435,
title = {Lattices properties of acyclic alternating pipe dreams},
author = {Noémie Cartier},
journal= {arXiv preprint arXiv:2311.10435},
year = {2023}
}
Comments
25 pages, 10 figures