Generalized permutahedra: Minkowski linear functionals and Ehrhart positivity

Autor:	Jochemko, Katharina, Ravichandran, Mohan
Rok vydání:	2019
Předmět:	Mathematics - Combinatorics Mathematics - Metric Geometry 05A15 52B12 (primary) 30C10 52B15 52B20 52B40 52B45 (secondary)
Druh dokumentu:	Working Paper
Popis:	We characterize all signed Minkowski sums that define generalized permutahedra, extending results of Ardila-Benedetti-Doker (2010). We use this characterization to give a complete classification of all positive, translation-invariant, symmetric Minkowski linear functionals on generalized permutahedra. We show that they form a simplicial cone and explicitly describe their generators. We apply our results to prove that the linear coefficients of Ehrhart polynomials of generalized permutahedra, which include matroid polytopes, are non-negative, verifying conjectures of De Loera-Haws-Koeppe (2009) and Castillo-Liu (2018) in this case. We also apply this technique to give an example of a solid-angle polynomial of a generalized permutahedron that has negative linear term and obtain inequalities for beta invariants of contractions of matroids. Comment: 16 pages; v3: minor revisions, Corollary 4.8 added; v4: 18 pages, introduction revised, further minor changes; accepted for publication in Mathematika
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1909.08448 Zobrazit plný text záznamu View this record from Arxiv