On Piecewise-Linear Homeomorphisms Between Distributive and Anti-blocking Polyhedra

Abstract

Stanley (1986) introduced the order polytope and chain polytope of a partially ordered set and showed that they are related by a piecewise-linear homeomorphism. In this paper we view order and chain polytopes as instances of distributive and anti-blocking polytopes, respectively. Both these classes of polytopes are defined in terms of the componentwise partial order on \(\mathbb {R}^n\). We generalize Stanley’s PL-homeomorphism to a large class of distributive polyhedra using infinite walks in marked networks.