Kevin O'Bryant

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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 = s1 + s2, si ∈ S; such sets are called Sidon sets if g = 2 and generalized Sidon sets (or B2[ ⌈ 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)
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)
A symmetric subset of the reals is one that remains invariant under some reflection x 7→ 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)
as N → ∞ is not transparent. The random walk ∑Nn=1 wn, where the wn are independent random variables taking the values ±1 with equal probability, is known [22] to typically have absolute value around c √ N , for an appropriate constant c and large N . Knowing this, and knowing that for irrational α the sequence ⌊nα⌋ is “random-ish” modulo 2, a natural guess(More)
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