Generalized permutahedra: Minkowski linear functionals and Ehrhart positivity
Generalized permutahedra: Minkowski linear functionals and Ehrhart positivity
We characterize all signed Minkowski sums that define generalized permutahedra, extending results of Ardila–Benedetti–Doker (Discrete Comput. Geom. 43 (2010), no. 4, 841–854). 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 …