منابع مشابه
Distribution of Points on Arcs
Let z1, . . . , zN be complex numbers situated on the unit circle |z| = 1, and write S := z1 + · · · + zN . Generalizing a well-known lemma by Freiman, we prove the following. (i) Suppose that any open arc of length φ ∈ (0, π] of the unit circle contains at most n of the numbers z1, . . . , zN . Then |S| ≤ 2n−N + 2(N − n) cos(φ/2). (ii) Suppose that any open arc of length π of the unit circle c...
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 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 ...
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We show that up to unimodular equivalence there are only finitely many d-dimensional lattice polytopes without interior lattice points that do not admit a lattice projection onto a (d− 1)-dimensional lattice polytope without interior lattice points. This was conjectured by Treutlein. As an immediate corollary, we get a short proof of a recent result of Averkov, Wagner &Weismantel, namely the fi...
متن کاملOn circular-arc graphs having a model with no three arcs covering the circle
An interval graph is the intersection graph of a finite set of intervals on a line and a circular-arc graph is the intersection graph of a finite set of arcs on a circle. While a forbidden induced subgraph characterization of interval graphs was found fifty years ago, finding an analogous characterization for circular-arc graphs is a long-standing open problem. In this work, we study the inters...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1991
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-59-1-87-90