Search Results - "RUZSA, IMRE Z."

Sumsets and entropy by Ruzsa, Imre Z.

“…We consider the connection and analogy between certain cardinality inequalities of combinatorial number theory and some entropy inequalities. We present a…”
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Beurling-Integers with Lacunarity by Ruzsa, Imre Z.

“…We present examples of multiplicative semigroups of positive reals (Beurling’s generalized integers) with gaps bounded from below…”
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An Analytic Approach to Cardinalities of Sumsets by Matolcsi, Dávid, Ruzsa, Imre Z., Shakan, George, Zhelezov, Dmitrii

“…Let d be a positive integer and U ⊂ ℤ d finite. We study β ( U ) : = inf A , B ≠ ϕ finite | A + B + U | | A | 1 / 2 | B | 1 / 2 , and other related quantities…”
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On the arithmetic Kakeya conjecture of Katz and Tao by Green, Ben, Ruzsa, Imre Z.

“…The arithmetic Kakeya conjecture, formulated by Katz and Tao (Math Res Lett 6(5–6):625–630, 1999 ), is a statement about addition of finite sets. It is known…”
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Difference Sets and Positive Exponential Sums. II: Cubic Residues in Cyclic Groups by Matolcsi, Máté, Ruzsa, Imre Z.

“…By constructing suitable nonnegative exponential sums, we give upper bounds on the cardinality of any set in cyclic groups such that the difference set avoids…”
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Difference Sets and Positive Exponential Sums I. General Properties by Matolcsi, Máté, Ruzsa, Imre Z.

“…We describe general connections between intersective properties of sets in Abelian groups and positive exponential sums. In particular, given a set A the…”
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Triangulations and a Discrete Brunn–Minkowski Inequality in the Plane by Böröczky, Károly J., Matolcsi, Máté, Ruzsa, Imre Z., Santos, Francisco, Serra, Oriol

“…For a set A of points in the plane, not all collinear, we denote by tr ( A ) the number of triangles in a triangulation of A , that is, tr ( A ) = 2 i + b - 2…”
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Sum-free sets in abelian groups by Green, Ben, Ruzsa, Imre Z.

“…LetA be a subset of an abelian groupG with |G|=n. We say thatA is sum-free if there do not existx, y, z εA withx+y=z. We determine, for anyG, the maximal…”
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Better Bounds for Planar Sets Avoiding Unit Distances by Keleti, Tamás, Matolcsi, Máté, de Oliveira Filho, Fernando Mário, Ruzsa, Imre Z.

“…A 1-avoiding set is a subset of  R n that does not contain pairs of points at distance 1. Let  m 1 ( R n ) denote the maximum fraction of  R n that can be…”
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Generalization of a theorem of Erdős and Rényi on Sidon sequences by Cilleruelo, Javier, Kiss, Sándor Z., Ruzsa, Imre Z., Vinuesa, Carlos

“…Erdős and Rényi claimed and Vu proved that for all h ≥ 2 and for all ϵ > 0, there exists g = gh(ϵ) and a sequence of integers A such that the number of ordered…”
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Euclidean algorithm in different norms by RUZSA, IMRE Z., VARJU, PETER P.

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Additive and multiplicative Sidon sets by Ruzsa, Imre Z.

“…Inspired by a paper of Sarkoezy [4] we study sets of integers and sets of residues with the property that all sums and all products are distinct…”
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Note on an Inequality of Wegner by Boroczky, Karoly J., Ruzsa, Imre Z.

“…Wegner gave a geometric characterization of all so-called Groemer packing of n greater than or equal to 2 unit discs in E 2 that are densest packings of n unit…”
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Convexity and Sumsets by Elekes, György, Nathanson, Melvyn B, Ruzsa, Imre Z

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An Infinite Sidon Sequence by Ruzsa, Imre Z

“…We show the existence of an infinite Sidon sequence such that the number of elements in [1,N] isN2−1+o(1)for all largeN…”
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Exact Additive Complements by Ruzsa, Imre Z.

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Minimum shadows in uniform hypergraphs and a generalization of the Takagi function by Frankl, Peter, Matsumoto, Makoto, Ruzsa, Imre Z, Tokushige, Norihide

“…The shadow function is closely related to the Kruskal-Katona Theorem. The Takagi function is a standard example of a nowhere differentiable continuous…”
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Freiman's theorem in an arbitrary abelian group by Green, Ben, Ruzsa, Imre Z.

“…A famous result of Freiman describes the structure of finite sets A ⊆ ℤ with small doubling property. If |A + A| ≤ K|A|, then A is contained within a…”
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Additive properties of dense subsets of sifted sequences by RAMARÉ, Olivier, RUZSA, Imre Z.

“…Nous nous intéressons aux propriétiés additives des soussuites de densité de suites "bien criblées" et montrons en particulier que, sous des hypothèses très…”
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Sets with no solutions to x+y=3z by Matolcsi, Máté, Ruzsa, Imre Z.

“…This short note gives an upper bound on the measure of sets A⊂[0,1] such that x+y=3z has no solutions in A…”
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