Year: 2025
Type: preprint
Abstract: For each permutation $w$, we consider the set $\mathrm{PD}(w)$ 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 $\mathrm{PD}(w)$ is a lattice. To establish this result, we provide a global description of the partial order on $\mathrm{PD}(w)$ by showing that $\mathrm{PD}(w)$ is isomorphic to a poset consisting of objects called Lehmer tableaux. In addition, we prove that $\mathrm{PD}(w)$ is a semidistributive polygonal lattice whose polygons are all diamonds or pentagons.
Source: arXiv (Cornell University)
Authors: Axelrod-Freed, Ilani, Defant, Colin, Mularczyk, Hanna, Nguyen, Son, Tung, Katherine
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415310475
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