On a special class of general permutahedra

2016/11/16 by Geir Agnarsson, Agnarsson, Geir · 1 citation
Mathematics · Engineering · Computer Science · #Advanced Combinatorial Mathematics #graph theory and CDMA systems #Coding theory and cryptography

paper · pdf · doi:10.48550/arxiv.1611.05314

Abstract

Minkowski sums of simplices in ℝⁿ form an interesting class of polytopes that seem to emerge in various situations. In this paper we discuss the Minkowski sum of the simplices Δ_k-1 in ℝⁿ where k and n are fixed, their flags and some of their face lattice structure. In particular, we derive a closed formula for their \em exponential generating flag function. These polytopes are simple, include both the simplex Δ_n-1 and the permutahedron Π_n-1, and form a Minkowski basis for more general permutahedra.

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