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arXiv · 2303.11025

Lattices of acyclic pipe dreams

Nantel Bergeron·Noémie Cartier·Cesar Ceballos·Vincent Pilaud
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Abstract

We show that for any permutation $ω$, the increasing flip graph on acyclic pipe dreams with exiting permutation $ω$ is a lattice quotient of the interval $[e,ω]$ of the weak order. We then discuss conjectural generalizations of this result to acyclic facets of subword complexes on arbitrary finite Coxeter groups.

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Nantel Bergeron, Noémie Cartier, Cesar Ceballos, Vincent Pilaud. 2025-02-20. Lattices of acyclic pipe dreams. https://doi.org/10.5802/alco.423

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