Chute Move Posets are Lattices
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908454955778048 |
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| author | Axelrod-Freed, Ilani Defant, Colin Mularczyk, Hanna Nguyen, Son Tung, Katherine |
| author_facet | Axelrod-Freed, Ilani Defant, Colin Mularczyk, Hanna Nguyen, Son Tung, Katherine |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chute Move Posets are Lattices Axelrod-Freed, Ilani Defant, Colin Mularczyk, Hanna Nguyen, Son Tung, Katherine Combinatorics 05A05, 06A07, 06B05, 06D75 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. |
| title | Chute Move Posets are Lattices |
| topic | Combinatorics 05A05, 06A07, 06B05, 06D75 |
| url | https://arxiv.org/abs/2507.13214 |