Alcoved polytopes. I.
type: Item
instance of: scholarly article
title: Alcoved polytopes. I.
zbMATH Open document ID: 1134.52019
author: Thomas Lam
author: Alexander Postnikov
published in: Discrete \& Computational Geometry
publication date: 2008-01-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0501246
review text: The hyperplanes of the affine Coxeter arrangement subdivide \(\mathbb{R}^{n-1}\) into unit simplices, called alcoves. An alcoved polytope is a convex polytope which is the union of some alcoves. Hypersimplices, order polytopes and some special matroid polytopes are examples of alcoved polytopes. In Section 2 of the present paper the authors show the equivalence of the triangulation of hypersimplices due to \textit{R. P. Stanley} [Higher Comb., Proc. NATO Adv. Study Inst., Berlin (West) 1976, 49 (1977; Zbl 0359.05001)] and \textit{B. Sturmfels} [Gröbner bases and convex polytopes. University Lecture Series. 8. Providence, RI: American Mathematical Society (AMS). (1996; Zbl 0856.13020)], the alcove triangulation and the new ``circuit triangulation''. Than they extend this triangulations to general alcoved polytopes and give a formula for the volume of an alcoved polytope. Finally, they study three special examples of alcoved polytopes.
Mathematics Subject Classification ID: 52B12
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 5223287
zbMATH Keywords: alcoved polytope
zbMATH Keywords: hypersimplex
zbMATH Keywords: triangulation
reviewed by: Eike Hertel
MaRDI profile type: Publication
OpenAlex ID: W2006093530
arXiv ID: math/0501246
DOI: 10.1007/S00454-006-1294-3
description: scientific article