Line Shellings of Geometric Lattices
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908754061033472 |
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| author | Backman, Spencer Dorpalen-Barry, Galen Nathanson, Anastasia Partida, Ethan Prime, Noah |
| author_facet | Backman, Spencer Dorpalen-Barry, Galen Nathanson, Anastasia Partida, Ethan Prime, Noah |
| contents | Inspired by Bruggesser-Mani's line shellings of polytopes, we introduce line shellings for the lattice of flats of a matroid: given a normal complex for a Bergman fan of a matroid induced by a building set, we show that the lexicographic order of the coordinates of its vertices is a shelling order. This gives a new proof of Björner's classical result that the order complex of the lattice of flats of a matroid is shellable, and demonstrates shellability for all nested set complexes for matroids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05119 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Line Shellings of Geometric Lattices Backman, Spencer Dorpalen-Barry, Galen Nathanson, Anastasia Partida, Ethan Prime, Noah Combinatorics 05E14, 05E45, 52B40, 52B22 Inspired by Bruggesser-Mani's line shellings of polytopes, we introduce line shellings for the lattice of flats of a matroid: given a normal complex for a Bergman fan of a matroid induced by a building set, we show that the lexicographic order of the coordinates of its vertices is a shelling order. This gives a new proof of Björner's classical result that the order complex of the lattice of flats of a matroid is shellable, and demonstrates shellability for all nested set complexes for matroids. |
| title | Line Shellings of Geometric Lattices |
| topic | Combinatorics 05E14, 05E45, 52B40, 52B22 |
| url | https://arxiv.org/abs/2601.05119 |