The numbers of edges of the order polytope and the chain polytope of a finite partially ordered set
| Autor: | Takayuki Hibi, Yoshimi Sahara, Nan Li, Akihiro Shikama |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Birkhoff polytope 010102 general mathematics Uniform k 21 polytope 01 natural sciences Theoretical Computer Science Combinatorics Convex polytope Cross-polytope Discrete Mathematics and Combinatorics Abstract polytope 0101 mathematics Ehrhart polynomial Partially ordered set Vertex enumeration problem Mathematics |
| Zdroj: | Discrete Mathematics. 340:991-994 |
| ISSN: | 0012-365X |
| DOI: | 10.1016/j.disc.2017.01.005 |
| Popis: | Let P be an arbitrary finite partially ordered set. It will be proved that the number of edges of the order polytope 풪 ( P ) is equal to that of the chain polytope C ( P ) . Furthermore, it will be shown that the degree sequence of the finite simple graph which is the 1 -skeleton of 풪 ( P ) is equal to that of C ( P ) if and only if 풪 ( P ) and C ( P ) are unimodularly equivalent. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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