Two poset polytopes

Abstract

Two convex polytopes, called the order polytope θ{symbol}(P) and chain polytope ℒ(P), are associated with a finite poset P. There is a close interplay between the combinatorial structure of P and the geometric structure of θ{symbol}(P). For instance, the order polynomial Ω(P, m) of P and Ehrhart polynomial i(θ{symbol}(P), m) of θ{symbol}(P) are related by Ω(P, m+1)=i(θ{symbol}(P), m). A "transfer map" then allows us to transfer properties of θ{symbol}(P) to ℒ(P). In particular, we transfer known inequalities involving linear extensions of P to some new inequalities. © 1986 Springer-Verlag New York Inc.