Lattice points in rational ellipsoids
نویسندگان
چکیده
منابع مشابه
Counting Lattice Points of Rational Polyhedra
The generating function F (P ) = ∑ α∈P∩ZN xα for a rational polytope P carries all essential information of P . In this paper we show that for any positive integer n, the generating function F (P, n) of nP = {nx : x ∈ P} can be written as F (P, n) = ∑ α∈A Pα(n)x, where A is the set of all vertices of P and each Pα(n) is a certain periodic function of n. The Ehrhart reciprocity law follows autom...
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We generalize Ehrhart’s idea ([Eh]) of counting lattice points in dilated rational polytopes: Given a rational simplex, that is, an n-dimensional polytope with n+ 1 rational vertices, we use its description as the intersection of n+ 1 halfspaces, which determine the facets of the simplex. Instead of just a single dilation factor, we allow different dilation factors for each of these facets. We ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2009
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2008.09.051