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- W2952479597 abstract "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 $tinZ_{ge 0}$, 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." @default.
- W2952479597 created "2019-06-27" @default.
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- W2952479597 date "2009-04-04" @default.
- W2952479597 modified "2023-09-27" @default.
- W2952479597 title "A finite calculus approach to Ehrhart polynomials" @default.
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