Alcoved Polytopes,I |
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Authors: | Thomas Lam Alexander Postnikov |
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Institution: | (1) Department of Mathematics, M.I.T., Cambridge, MA 02139, USA |
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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. |
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