Ordinal pattern probabilities for symmetric random walks equal combinatorial counts in affine Weyl groups for uniform steps and level-function products for Laplace steps.
Alcoved Polytopes II
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
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 A_n, C_n and D_4, we give a Grobner basis which induces the triangulation of alcoved polytopes.
fields
math.CO 2verdicts
UNVERDICTED 2representative citing papers
Constructs a hypersimplicial subdivision of a dilated hypersimplex to give a geometric proof of the Brenti-Welker identity.
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Ordinal pattern probabilities for symmetric random walks
Ordinal pattern probabilities for symmetric random walks equal combinatorial counts in affine Weyl groups for uniform steps and level-function products for Laplace steps.
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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.