Séminaire Lotharingien de Combinatoire, 95B.61 (2026), 12 pp.
Ilani Axelrod-Freed, Sara Billey, Colin Defant, Connor McCausland, Clare Minnerath, Hanna Mularczyk, Son Nguyen and Katherine Tung
Two Proofs of Rubey's Lattice Conjecture
Abstract.
In 2012, Rubey introduced a natural partial order on the set of
reduced pipe dreams of a permutation in which cover relations
correspond to generalized chute moves. He conjectured that this poset
is a lattice. We discuss two proofs of Rubey's conjecture that we
found independently and simultaneously in two groups. In addition, we
show that this lattice is semidistributive and polygonal. A simple
test for comparison in the Rubey lattice is given in terms of tableaux
associated to reduced pipe dreams.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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