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Alcoved Polytopes II

2012/02/17 by Thomas Lam, Lam, Thomas, Alexander Postnikov +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1202.4015

Abstract

This is the second of two papers where we study polytopes arising from affine Coxeter arrangements. Our results include a formula for their volumes, and also compatible definitions of hypersimplices, descent numbers and major index for all Weyl groups. We give a q-analogue of Weyl's formula for the order of the Weyl group. For An, Cn and D4, we give a Grobner basis which induces the triangulation of alcoved polytopes.

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