The Tropical Division Problem and the Minkowski Factorization of Generalized Permutahedra

Autor:	Crowell, Robert Alexander
Rok vydání:	2019
Předmět:	Mathematics - Combinatorics Computer Science - Computational Geometry 13P05 52B20 14T05 52B40 20F55
Druh dokumentu:	Working Paper
Popis:	Given two tropical polynomials $f, g$ on $\mathbb{R}^n$, we provide a characterization for the existence of a factorization $f= h \odot g$ and the construction of $h$. As a ramification of this result we obtain a parallel result for the Minkowski factorization of polytopes. Using our construction we show that for any given polytopal fan there is a polytope factorization basis, i.e. a finite set of polytopes with respect to which any polytope whose normal fan is refined by the original fan can be uniquely written as a signed Minkowski sum. We explicitly study the factorization of polymatroids and their generalizations, Coxeter matroid polytopes, and give a hyperplane description of the cone of deformations for this class of polytopes. Comment: 25 pages, 9 Figures, 2 Tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1908.00241 Zobrazit plný text záznamu View this record from Arxiv