Convex polytopes all of whose reverse lexicographic initial ideals are squarefree

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 ) (0,1) -polytope to be compressed will be presented. One of its immediate consequences is that the class of compressed ( 0 , 1 ) (0,1) -polytopes includes (i) hypersimplices, (ii) order polytopes of finite partially ordered sets, and (iii) stable polytopes of perfect graphs.