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no. 3
Lattices of acyclic pipe dreams
Bergeron, Nantel1; Cartier, Noémie2; Ceballos, Cesar3; Pilaud, Vincent4
1 Department of Mathematics and Statistics York University Toronto Canada
2 LISN Université Paris Saclay France
3 Institute of Geometry Technische Universität Graz Austria
4 Universitat de Barcelona & Centre de Recerca Matemàtica Barcelona Spain
Algebraic Combinatorics, Volume 8 (2025) no. 3, pp. 817-856.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.423
Classification: 06A07, 06B10, 20F55
Keywords: lattices, lattice congruences, pipe dreams, subword complexes

Bergeron, Nantel 1; Cartier, Noémie 2; Ceballos, Cesar 3; Pilaud, Vincent 4

1 Department of Mathematics and Statistics York University Toronto Canada
2 LISN Université Paris Saclay France
3 Institute of Geometry Technische Universität Graz Austria
4 Universitat de Barcelona & Centre de Recerca Matemàtica Barcelona Spain
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Bergeron, Nantel; Cartier, Noémie; Ceballos, Cesar; Pilaud, Vincent. Lattices of acyclic pipe dreams. Algebraic Combinatorics, Volume 8 (2025) no. 3, pp. 817-856. doi : 10.5802/alco.423. https://alco.centre-mersenne.org/articles/10.5802/alco.423/

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