A finite calculus approach to Ehrhart polynomials

Details A finite calculus approach to Ehrhart polynomials A finite calculus approach to Ehrhart polynomials

2009-04-04

arxiv.org/abs/0904.0679v2

Electron. J. Combin. 17 (2010), no. 1, Research Paper 68, 13pp.

Mathematics

Combinatorics

13 pages, 1 figure; v2: added examples and Section 4, final version

Scientific paper

A rational polytope is the convex hull of a finite set of points in $\R^d$ with rational coordinates. Given a rational polytope $P \subseteq \R^d$, Ehrhart proved that, for $t\in\Z_{\ge 0}$, the function $#(tP \cap \Z^d)$ agrees with a quasi-polynomial $L_P(t)$, called the Ehrhart quasi-polynomial. The Ehrhart quasi-polynomial can be regarded as a discrete version of the volume of a polytope. We use that analogy to derive a new proof of Ehrhart's theorem. This proof also allows us to quickly prove two other facts about Ehrhart quasi-polynomials: McMullen's theorem about the periodicity of the individual coefficients of the quasi-polynomial and the Ehrhart-Macdonald theorem on reciprocity.

Affiliated with

Also associated with

No associations

Rating

A finite calculus approach to Ehrhart polynomials 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 A finite calculus approach to Ehrhart polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A finite calculus approach to Ehrhart polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-123009