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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	817-856
Number of pages	40
Journal	Algebraic Combinatorics
Volume	8
Issue number	3
DOIs	https://doi.org/10.5802/alco.423
Publication status	Published - 1 Jan 2025
Externally published	Yes

Keywords

lattice congruences
lattices
pipe dreams
subword complexes

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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.",

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AU - Bergeron, Nantel

AU - Cartier, Noémie

AU - Ceballos, Cesar

AU - Pilaud, Vincent

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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

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DO - 10.5802/alco.423

M3 - Article

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JF - Algebraic Combinatorics

IS - 3

ER -

Lattices of acyclic pipe dreams

Abstract

Keywords

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