Alcoved Polytopes I

Details Alcoved Polytopes I Alcoved Polytopes I

2005-01-16

arxiv.org/abs/math/0501246v2

Mathematics

Combinatorics

Paper reorganized. Final version. 23 pages

Scientific paper

The aim of this paper is to study alcoved polytopes, which are polytopes arising from affine Coxeter arrangements. This class of convex polytopes includes many classical polytopes, for example, the hypersimplices. We compare two constructions of triangulations of hypersimplices due to Stanley and Sturmfels and explain them in terms of alcoved polytopes. We study triangulations of alcoved polytopes, the adjacency graphs of these triangulations, and give a combinatorial formula for volumes of these polytopes. In particular, we study a class of matroid polytopes, which we call the multi-hypersimplices.

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