Mathematics – Combinatorics
Scientific paper
2007-05-08
Eur. J. Comb. 29 (2008), 1596-1602
Mathematics
Combinatorics
AMS-LaTeX, 9 pages; introduction improved
Scientific paper
10.1016/j.ejc.2007.11.002
The h^*-polynomial of a lattice polytope is the numerator of the generating function of the Ehrhart polynomial. Let P be a lattice polytope with h^*-polynomial of degree d and with linear coefficient h^*_1. We show that P has to be a lattice pyramid over a lower-dimensional lattice polytope, if the dimension of P is greater or equal to h^*_1 (2d+1) + 4d-1. This result has a purely combinatorial proof and generalizes a recent theorem of Batyrev.
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