A Continuous Family of Marked Poset Polytopes

authored by

Xin Fang, Ghislain Fourier, Jan-philipp Litza, Christoph Pegel

Abstract

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 transfer maps, we show that the vertices of the hypercube parametrize an Ehrhart equivalent family of lattice polytopes. The combinatorial type of the polytopes is constant when the parameters vary in the relative interior of each face of the hypercube. Moreover, with the help of a subdivision arising from a tropical hyperplane arrangement associated to the marked poset, we give an explicit description of the vertices of the polytope for generic parameters.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

RWTH Aachen University
University of Cologne
University of Bremen

Type

Article

Journal

SIAM Journal on Discrete Mathematics

Volume

34

Pages

611-639

No. of pages

29

ISSN

0895-4801

Publication date

03.03.2020

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Mathematics(all)

Electronic version(s)

https://doi.org/10.48550/arXiv.1712.01037 (Access: Open)
https://doi.org/10.1137/18M1228529 (Access: Closed)