| Autor: |
Swee Hong Chan, Igor Pak |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
|
| Zdroj: |
Forum of Mathematics, Pi, Vol 12 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2050-5086 |
| DOI: |
10.1017/fmp.2024.20 |
| Popis: |
Describing the equality conditions of the Alexandrov–Fenchel inequality [Ale37] has been a major open problem for decades. We prove that in the case of convex polytopes, this description is not in the polynomial hierarchy unless the polynomial hierarchy collapses to a finite level. This is the first hardness result for the problem and is a complexity counterpart of the recent result by Shenfeld and van Handel [SvH23], which gave a geometric characterization of the equality conditions. The proof involves Stanley’s [Sta81] order polytopes and employs poset theoretic technology. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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