Higher integrality conditions, volumes and Ehrhart polynomials |
| |
Authors: | Fu Liu |
| |
Institution: | Department of Mathematics, University of California, One Shields Avenue, Davis, CA 95616, United States |
| |
Abstract: | A polytope is integral if all of its vertices are lattice points. The constant term of the Ehrhart polynomial of an integral polytope is known to be 1. In previous work, we showed that the coefficients of the Ehrhart polynomial of a lattice-face polytope are volumes of projections of the polytope. We generalize both results by introducing a notion of k-integral polytopes, where 0-integral is equivalent to integral. We show that the Ehrhart polynomial of a k-integral polytope P has the properties that the coefficients in degrees less than or equal to k are determined by a projection of P, and the coefficients in higher degrees are determined by slices of P. A key step of the proof is that under certain generality conditions, the volume of a polytope is equal to the sum of volumes of slices of the polytope. |
| |
Keywords: | MSC: primary 52B20 secondary 52A38 05A15 |
本文献已被 ScienceDirect 等数据库收录! |
|