Lattices of acyclic pipe dreams
Nantel Bergeron, Noémie Cartier, Cesar Ceballos, Vincent Pilaud
Published: 2023/3/20
Abstract
We show that for any permutation $\omega$, the increasing flip graph on acyclic pipe dreams with exiting permutation $\omega$ is a lattice quotient of the interval $[e,\omega]$ of the weak order. We then discuss conjectural generalizations of this result to acyclic facets of subword complexes on arbitrary finite Coxeter groups.