منابع مشابه
A Combinatorial Property of Points anf Ellipsoids
For each d-1 there is a constant Ca > 0 such that any finite set X c R a contains a subset YcX, IYI<-[~d(d+3)J +1 having the following property: if E = Y is an ellipsoid, then IE nXt-> c~JXl.
متن کاملLattice Points in Lattice Polytopes
We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩lZ (provided it is non-empty) contains a point whose coefficient ofasymmetry with respect to P is at most 8d · (8l+7)2d+1. If, moreover,P is a simplex, then this bound can be improved to 8 · (8l+ 7)d+1.As an application, we deduce new upper bounds on the volume ofa lattice polytope, given its ...
متن کاملLattice Points inside Lattice Polytopes
We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩ lZ (provided it is non-empty) contains a point whose coefficient of asymmetry with respect to P is at most 8d · (8l+7) 2d+1 . If, moreover, P is a simplex, then this bound can be improved to 9 · (8l+ 7) d+1 . This implies that the maximum volume of a lattice polytope P ⊂ R d containing exactly k ≥ 1 points of lZ in its interior, is...
متن کاملLattice Points in Minkowski Sums
Fakhruddin has proved that for two lattice polygons P and Q any lattice point in their Minkowski sum can be written as a sum of a lattice point in P and one in Q, provided P is smooth and the normal fan of P is a subdivision of the normal fan of Q. We give a shorter combinatorial proof of this fact that does not need the smoothness assumption on P .
متن کاملLattice Points in Simple Polytopes
P (h) φ(x)dx where the polytope P (h) is obtained from P by independent parallel motions of all facets. This extends to simple lattice polytopes the EulerMaclaurin summation formula of Khovanskii and Pukhlikov [8] (valid for lattice polytopes such that the primitive vectors on edges through each vertex of P form a basis of the lattice). As a corollary, we recover results of Pommersheim [9] and ...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1991
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-59-4-329-338