Alcoved Polytopes II
classification
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polytopesweylalcovedformulagiveaffinearisingarrangements
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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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Cited by 1 Pith paper
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A geometric proof of the Brenti--Welker identity
Constructs a hypersimplicial subdivision of a dilated hypersimplex to give a geometric proof of the Brenti-Welker identity.
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