Computing the Ehrhart quasi-polynomial of a rational simplex
Combinatorics
2007-05-23 v1 Metric Geometry
Abstract
We present a polynomial time algorithm to compute any fixed number of the highest coefficients of the Ehrhart quasi-polynomial of a rational simplex. Previously such algorithms were known for integer simplices and for rational polytopes of a fixed dimension. The algorithm is based on the formula relating the kth coefficient of the Ehrhart quasi-polynomial of a rational polytope to volumes of sections of the polytope by affine lattice subspaces parallel to k-dimensional faces of the polytope. We discuss possible extensions and open questions.
Cite
@article{arxiv.math/0504444,
title = {Computing the Ehrhart quasi-polynomial of a rational simplex},
author = {Alexander Barvinok},
journal= {arXiv preprint arXiv:math/0504444},
year = {2007}
}
Comments
21 pages