Ilani Axelrod-Freed (MIT)

Title: The Chute Moves Lattice.

Abstract:  For each permutation w, we consider the set RP(w) of reduced pipe dreams for w, partially ordered so that cover relations correspond to (generalized) chute moves. Settling a conjecture of Rubey from 2012, we prove that RP(w) is a lattice. To establish this result, introduce another poset consisting of objects called Lehmer tableaux with relation given by entrywise comparison. We provide a global description of the partial order on RP(w) by showing that these two posets are isomorphic. In addition, we prove that RP(w) is a semidistributive polygonal lattice whose polygons are all diamonds or pentagons.

Room PK-4323 of UQAM’s Président-Kennedy Building.