Lattices of acyclic pipe dreams

Nantel Bergeron; Noémie Cartier; Cesar Ceballos; Vincent Pilaud

doi:10.5802/alco.423

Lattices of acyclic pipe dreams

Nantel Bergeron
, Noémie Cartier
, Cesar Ceballos
, Vincent Pilaud

York University
Université Paris-Saclay
Graz University of Technology
University of Barcelona

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	817-856
Nombre de pages	40
journal	Algebraic Combinatorics
Volume	8
Numéro de publication	3
Les DOIs	https://doi.org/10.5802/alco.423
état	Publié - 1 janv. 2025
Modification externe	Oui

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10.5802/alco.423

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title = "Lattices of acyclic pipe dreams",

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.",

keywords = "lattice congruences, lattices, pipe dreams, subword complexes",

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AU - Bergeron, Nantel

AU - Cartier, Noémie

AU - Ceballos, Cesar

AU - Pilaud, Vincent

N1 - Publisher Copyright: © The author(s), 2025.

PY - 2025/1/1

Y1 - 2025/1/1

N2 - 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.

AB - 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.

KW - lattice congruences

KW - lattices

KW - pipe dreams

KW - subword complexes

UR - https://www.scopus.com/pages/publications/105011244653

U2 - 10.5802/alco.423

DO - 10.5802/alco.423

M3 - Article

AN - SCOPUS:105011244653

SN - 2589-5486

VL - 8

SP - 817

EP - 856

JO - Algebraic Combinatorics

JF - Algebraic Combinatorics

IS - 3

ER -

Lattices of acyclic pipe dreams

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