Ehrhart h[superscript ∗]-Vectors of Hypersimplices
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454_2012_Article_9452.pdf
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1.09 MB
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Author(s)
Li, Nan
Alternative Title
Ehrhart h ∗-Vectors of Hypersimplices
Date Issued
August 2012
Journal
Discrete & Computational Geometry
Publisher
Springer-Verlag
Citation
Li, Nan. “Ehrhart H ∗-Vectors of Hypersimplices.” Discrete & Computational Geometry (2012): n. pag.
Version
Author's final manuscript
Abstract
We consider the Ehrhart h[superscript ∗]-vector for the hypersimplex. It is well-known that the sum of the h[superscript ∗][subscript i] is the normalized volume which equals the Eulerian numbers. The main result is a proof of a conjecture by R. Stanley which gives an interpretation
of the h[superscript ∗][subscript i] coefficients in terms of descents and exceedances. Our proof is geometric using a careful book-keeping of a shelling of a unimodular triangulation. We generalize this result to other closely related polytopes.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s00454-012-9452-2
