Alcoved Polytopes II

Details Alcoved Polytopes II Alcoved Polytopes II

2012-02-17

arxiv.org/abs/1202.4015v1

Mathematics

Combinatorics

17 pages

Scientific paper

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 A_n, C_n and D_4, we give a Grobner basis which induces the triangulation of alcoved polytopes.

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