Mixed volumes of zonoids and the absolute value of the Grassmannian

Autor:	Averkov, Gennadiy, von Dichter, Katherina, Richard, Simon, Soprunov, Ivan
Rok vydání:	2024
Předmět:	Mathematics - Combinatorics Mathematics - Algebraic Geometry Mathematics - Metric Geometry
Druh dokumentu:	Working Paper
Popis:	Zonoids are Hausdorff limits of zonotopes, while zonotopes are convex polytopes defined as the Minkowski sums of finitely many segments. We present a combinatorial framework that links the study of mixed volumes of zonoids (a topic that has applications in algebraic combinatorics) with the study of the absolute value of the Grassmannian, defined as the image of the Grassmannian under the coordinate-wise absolute value map. We use polyhedral computations to derive new families of inequalities for n zonoids in dimension d, when (n,d)=(6,2) and (6,3). Unlike the classical geometric inequalities, originating from the Brunn-Minkowski and Aleksandrov-Fenchel inequalities, the inequalities we produce have the special feature of being Minkowski linear in each of the n zonoids they involve. Comment: 15 pages, 8 figures; full version of the paper replacing previously submitted extended abstract for MEGA 2024 conference
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.02842 Zobrazit plný text záznamu View this record from Arxiv