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DCG
2007

Alcoved Polytopes, I

13 years 3 months ago
Alcoved Polytopes, I
The aim of this paper is to initiate the study of 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.
Thomas Lam, Alexander Postnikov
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where DCG
Authors Thomas Lam, Alexander Postnikov
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