Ehrhart h∗-Vectors of Hypersimplices
N Li - Discrete & Computational Geometry, 2012 - Springer
We consider the Ehrhart h∗-vector for the hypersimplex. It is well-known that the sum of the
h_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^*_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.
h_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^*_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.
Ehrhart -vectors of hypersimplices
N Li - Discrete Mathematics & Theoretical Computer …, 2013 - dmtcs.episciences.org
We consider the Ehrhart $ h^* $-vector for the hypersimplex. It is well-known that the sum of
the $ h_i^* $ is the normalized volume which equals an Eulerian number. The main result is
a proof of a conjecture by R. Stanley which gives an interpretation of the $ h^* _i $
coefficients in terms of descents and excedances. 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.
the $ h_i^* $ is the normalized volume which equals an Eulerian number. The main result is
a proof of a conjecture by R. Stanley which gives an interpretation of the $ h^* _i $
coefficients in terms of descents and excedances. 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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