Lattices of acyclic pipe dreams

Abstract

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.

35 pages, 20 figures. Version 3: Corrections from referee

References in corpus (8)

• Cambrian Lattices
• The brick polytope of a sorting network
• Multitriangulations, pseudotriangulations and primitive sorting networks
• Brick polytopes of spherical subword complexes and generalized associahedra
• Subword complexes, cluster complexes, and generalized multi-associahedra
• Brick polytopes, lattice quotients, and Hopf algebras
• Catalan numbers and Schubert polynomials for $w=1(n+1)...2$
• The weak order on integer posets