The Ehrhart polynomial of a lattice 𝑛 -simplex

Diaz, Ricardo¹ ; Robins, Sinai²

¹ Department of Mathematics, University of Northern Colorado, Greeley, Colorado 80639
² Department of Mathematics, UCSD 9500 Gilman Drive, La Jolla, CA 92093-0112

Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 1, pp. 1-6.

Résumé

The problem of counting the number of lattice points inside a lattice polytope in $\mathbb {R}^{n}$ has been studied from a variety of perspectives, including the recent work of Pommersheim and Kantor-Khovanskii using toric varieties and Cappell-Shaneson using Grothendieck-Riemann-Roch. Here we show that the Ehrhart polynomial of a lattice $n$-simplex has a simple analytical interpretation from the perspective of Fourier Analysis on the $n$-torus. We obtain closed forms in terms of cotangent expansions for the coefficients of the Ehrhart polynomial, that shed additional light on previous descriptions of the Ehrhart polynomial.

Détail

DOI : 10.1090/S1079-6762-96-00001-7

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