Convex polytopes all of whose reverse lexicographic initial ideals are squarefree

Ohsugi, Hidefumi; Hibi, Takayuki

doi:10.1090/S0002-9939-01-05853-1

Convex polytopes all of whose reverse lexicographic initial ideals are squarefree
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by Hidefumi Ohsugi and Takayuki Hibi PDF

Proc. Amer. Math. Soc. 129 (2001), 2541-2546 Request permission

Abstract:

A compressed polytope is an integral convex polytope any of whose reverse lexicographic initial ideals is squarefree. A sufficient condition for a $(0,1)$-polytope to be compressed will be presented. One of its immediate consequences is that the class of compressed $(0,1)$-polytopes includes (i) hypersimplices, (ii) order polytopes of finite partially ordered sets, and (iii) stable polytopes of perfect graphs.

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