Self-Reachable Configuration Polytopes for Trees
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910601414967296 |
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| author | Lyons, Benjamin Olsen, McCabe |
| author_facet | Lyons, Benjamin Olsen, McCabe |
| contents | We study lattice polytopes which arise as the convex hull of chip vectors for \textit{self-reachable} chip configurations on a tree $T$. We show that these polytopes always have the integer decomposition property and characterize the vertex sets of these polytopes. Additionally, in the case of self-reachable configurations with the smallest possible number of chips, we show that these polytopes are unimodularly equivalent to a unit cube. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07675 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Self-Reachable Configuration Polytopes for Trees Lyons, Benjamin Olsen, McCabe Combinatorics 52B20, 05C57, 05C05 We study lattice polytopes which arise as the convex hull of chip vectors for \textit{self-reachable} chip configurations on a tree $T$. We show that these polytopes always have the integer decomposition property and characterize the vertex sets of these polytopes. Additionally, in the case of self-reachable configurations with the smallest possible number of chips, we show that these polytopes are unimodularly equivalent to a unit cube. |
| title | Self-Reachable Configuration Polytopes for Trees |
| topic | Combinatorics 52B20, 05C57, 05C05 |
| url | https://arxiv.org/abs/2409.07675 |