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We give explicit constructions of sets S with the property that for each integer k, there are at most g solutions to k = s 1 + s 2 , s i ∈ S; such sets are called Sidon sets if g = 2 and generalized Sidon sets (or B 2 [ g/2 ] sets) if g ≥ 3. We extend to generalized Sidon sets the Sidon-set constructions of Singer, Bose, and Ruzsa. We also further optimize… (More)

A symmetric subset of the reals is one that remains invariant under some reflection x → c − x. We consider, for any 0 < ε ≤ 1, the largest real number ∆(ε) such that every subset of [0, 1] with measure greater than ε contains a symmetric subset with measure ∆(ε). In this paper we establish upper and lower bounds for ∆(ε) of the same order of magnitude: for… (More)

An edge-labeling f of a graph G is an injection from E(G) to the set of integers. The edge-bandwidth of G is B 0 (G) = min f fB 0 (f)g, where B 0 (f) is the maximum diierence between labels of incident edges of G. The m-theta graph (l 1 ; : : : ; l m g is the graph consisting of m pairwise internally disjoint paths with common endpoints and lengths l 1 l m.… (More)

In 1946, Behrend gave a construction of dense finite sets of integers that do not contain 3-term arithmetic progressions. In 1961, Rankin generalized Behrend's construction to sets avoiding k-term arithmetic progressions, and in 2008 Elkin refined Behrend's 3-term construction. In this work, we combine Elkin's refinement and Rankin's generalization.… (More)

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