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arXiv · 2507.13214

Chute Move Posets are Lattices

Ilani Axelrod-Freed·Colin Defant·Hanna Mularczyk·Son Nguyen·Katherine Tung
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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.

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Ilani Axelrod-Freed, Colin Defant, Hanna Mularczyk, Son Nguyen, Katherine Tung. 2025-07-17. Chute Move Posets are Lattices. https://arxiv.org/abs/2507.13214

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