The expansion of half-integral polytopes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929252565254144 |
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| author | Cardinal, Jean Pournin, Lionel |
| author_facet | Cardinal, Jean Pournin, Lionel |
| contents | The expansion of a polytope is an important parameter for the analysis of the random walks on its graph. A conjecture of Mihai and Vazirani states that all $0/1$-polytopes have expansion at least 1. We show that the generalization to half-integral polytopes does not hold by constructing $d$-dimensional half-integral polytopes whose expansion decreases exponentially fast with $d$. We also prove that the expansion of half-integral zonotopes is uniformly bounded away from $0$. As an intermediate result, we show that half-integral zonotopes are always graphical. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14343 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The expansion of half-integral polytopes Cardinal, Jean Pournin, Lionel Combinatorics Computational Geometry Discrete Mathematics Metric Geometry The expansion of a polytope is an important parameter for the analysis of the random walks on its graph. A conjecture of Mihai and Vazirani states that all $0/1$-polytopes have expansion at least 1. We show that the generalization to half-integral polytopes does not hold by constructing $d$-dimensional half-integral polytopes whose expansion decreases exponentially fast with $d$. We also prove that the expansion of half-integral zonotopes is uniformly bounded away from $0$. As an intermediate result, we show that half-integral zonotopes are always graphical. |
| title | The expansion of half-integral polytopes |
| topic | Combinatorics Computational Geometry Discrete Mathematics Metric Geometry |
| url | https://arxiv.org/abs/2402.14343 |