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07 February 2025
 
  » arxiv » 1508.0187

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The numbers of edges of the order polytope and the chain poyltope of a finite partially ordered set
Takayuki Hibi ; Nan Li ; Yoshimi Sahara ; Akihiro Shikama ;
Date 2 Aug 2015
AbstractLet $P$ be an arbitrary finite partially ordered set. It will be proved that the number of edges of the order polytope ${mathcal O}(P)$ is equal to that of the chain polytope ${mathcal C}(P)$. Furthermore, it will be shown that the degree sequence of the finite simple graph which is the $1$-skeleton of ${mathcal O}(P)$ is equal to that of ${mathcal C}(P)$ if and only if ${mathcal O}(P)$ and ${mathcal C}(P)$ are unimodularly equivalent.
Source arXiv, 1508.0187
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