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On piecewise-linear homeomorphisms between distributive and anti-blocking polyhedra
Christoph Pegel, Raman Sanyal
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 vi…
The Minkowski Property and Reflexivity of Marked Poset Polytopes
Xin Fang, Ghislain Fourier, Christoph Pegel
We provide a Minkowski sum decomposition of marked chain-order polytopes into building blocks associated to elementary markings and thus give an explicit minimal set of generators…
Vertex-Maximal Lattice Polytopes Contained in 2-Simplices
Jan-Philipp Litza, Christoph Pegel, Kirsten Schmitz
Motivated by the problem of bounding the number of rays of plane tropical curves we study the following question: Given and a unimodular -simplex what is th…
A Continuous Family of Marked Poset Polytopes
Xin Fang, Ghislain Fourier, Jan-Philipp Litza +1
For any marked poset we define a continuous family of polytopes, parametrized by a hypercube, generalizing the notions of marked order and marked chain polytopes. By providing tran…