Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory

Details Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory

2010-11-27

arxiv.org/abs/1011.6002v1

Mathematics

Combinatorics

24 pages, 3 figures

Scientific paper

We study intermediate sums, interpolating between integrals and discrete sums, which were introduced by A. Barvinok [Computing the Ehrhart quasi-polynomial of a rational simplex, Math. Comp. 75 (2006), 1449--1466]. For a given semi-rational polytope P and a rational subspace L, we integrate a given polynomial function h over all lattice slices of the polytope P parallel to the subspace L and sum up the integrals. We first develop an algorithmic theory of parametric intermediate generating functions. Then we study the Ehrhart theory of these intermediate sums, that is, the dependence of the result as a function of a dilation of the polytope. We provide an algorithm to compute the resulting Ehrhart quasi-polynomials in the form of explicit step polynomials. These formulas are naturally valid for real (not just integer) dilations and thus provide a direct approach to real Ehrhart theory.

Affiliated with

Also associated with

No associations

Rating

Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Intermediate Sums on Polyhedra: Computation and Real Ehrhart Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-321252