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arXiv · 1911.12090

On piecewise-linear homeomorphisms between distributive and anti-blocking polyhedra

Christoph Pegel·Raman Sanyal
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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.

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Christoph Pegel, Raman Sanyal. 2019-11-27. On piecewise-linear homeomorphisms between distributive and anti-blocking polyhedra. https://arxiv.org/abs/1911.12090

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