Séminaire Lotharingien de Combinatoire, 89B.58 (2023), 12 pp.
Noémie Cartier
Acyclic Pipe Dreams, Subword Complexes and Lattice Quotients of Weak Order Intervals
Abstract.
The Tamari lattice is a well-known quotient of the weak order on permutations, and can be realized as the increasing flip poset of a family of pipe dreams with a well-chosen exit permutation. We show that for any permutation ω, the increasing flip poset on acyclic pipe dreams with exit permutation ω is a lattice quotient of the interval [id, ω] of the weak order. We then give similar quotients on acyclic pipe dreams on a family of non-triangular shapes. We finally discuss conjectural generalizations of these results to acyclic facets of subword complexes on any finite Coxeter group.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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