Kalai's $3^{d}$ conjecture for unconditional and locally anti-blocking polytopes
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914763354669056 |
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| author | Sanyal, Raman Winter, Martin |
| author_facet | Sanyal, Raman Winter, Martin |
| contents | Kalai's $3^d$ conjecture states that every centrally-symmetric $d$-polytope has at least $3^d$ faces. We give short proofs for two special cases: if $P$ is unconditional (that is, invariant w.r.t. reflection in any coordinate hyperplane), and more generally, if $P$ is locally anti-blocking. In both cases we show that the minimum is attained exactly for the Hanner polytopes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_02909 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Kalai's $3^{d}$ conjecture for unconditional and locally anti-blocking polytopes Sanyal, Raman Winter, Martin Combinatorics Discrete Mathematics Metric Geometry 51M20, 52B05, 52B11, 52B12, 52B15 Kalai's $3^d$ conjecture states that every centrally-symmetric $d$-polytope has at least $3^d$ faces. We give short proofs for two special cases: if $P$ is unconditional (that is, invariant w.r.t. reflection in any coordinate hyperplane), and more generally, if $P$ is locally anti-blocking. In both cases we show that the minimum is attained exactly for the Hanner polytopes. |
| title | Kalai's $3^{d}$ conjecture for unconditional and locally anti-blocking polytopes |
| topic | Combinatorics Discrete Mathematics Metric Geometry 51M20, 52B05, 52B11, 52B12, 52B15 |
| url | https://arxiv.org/abs/2308.02909 |