Ehrhart h[superscript ∗]-Vectors of Hypersimplices
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[supers...
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Format: | Article |
Language: | English |
Published: |
Springer-Verlag
2017
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Online Access: | http://hdl.handle.net/1721.1/109863 |
Summary: | 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. |
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