The Minkowski Property and Reflexivity of Marked Poset Polytopes
Xin Fang, Ghislain Fourier, Christoph Pegel
TL;DR
This paper characterizes when marked chain-order polytopes are reflexive, providing a Minkowski sum decomposition into elementary parts and identifying minimal generators of related semi-group algebras.
Contribution
It introduces a Minkowski sum decomposition for marked chain-order polytopes and characterizes reflexivity in terms of the underlying poset being ranked.
Findings
Minkowski sum decomposition into elementary building blocks
Explicit minimal generators for the semi-group algebra
Reflexivity characterized by the poset being ranked
Abstract
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 of an associated semi-group algebra. We proceed by characterizing the reflexive polytopes among marked chain-order polytopes as those with the underlying marked poset being ranked.
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