Additive number theory and inequalities in Ehrhart theory

Details Additive number theory and inequalities in Ehrhart theory Additive number theory and inequalities in Ehrhart theory

2009-04-20

arxiv.org/abs/0904.3035v2

Mathematics

Combinatorics

40 pages, 7 figures. Replaces `Kneser's theorem and inequalities in Ehrhart theory'. Improved dimension bounds

Scientific paper

We introduce a powerful connection between Ehrhart theory and additive number theory, and use it to produce infinitely many new classes of inequalities between the coefficients of the $h^*$-polynomial of a lattice polytope. This greatly improves upon the three known classes of inequalities, which were proved using techniques from commutative algebra and combinatorics. As an application, we deduce all possible `balanced' inequalities between the coefficients of the $h^*$-polynomial of a lattice polytope containing an interior lattice point, in dimension at most 6.

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