Alcoved Polytopes, I

Authors:
Thomas Lam;Alexander Postnikov
Affiliations:
Department of Mathematics, M.I.T., Cambridge, MA 02139, USA;Department of Mathematics, M.I.T., Cambridge, MA 02139, USA
Venue:
Discrete & Computational Geometry
Year:
2007

Citing 0
Cited 4

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Looping of the numbers game and the alcoved hypercube

Journal of Combinatorial Theory Series A

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Abstract

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.