26 citations · 53 across the 6 of their papers we have counts for
5 papers · 1 filter
Constructions of Generalized Sidon Sets
Greg Martin, Kevin O'Bryant
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\in S; such sets are called Sidon sets if g=2 and…
A Complete Annotated Bibliography of Work Related to Sidon Sequences
Kevin O'Bryant
A Sidon sequence is a sequence of integers a_1 < a_2 < a_3 < ... with the property that the sums a_i+a_j (i\le j) are distinct. This work contains a survey of Sidon sequences and t…
Almost Alternating Sums
Kevin O'Bryant, Bruce Reznick, Monika Serbinowska
Writing for a general mathematical audience, we provide elementary upper and lower bounds on the growth (as a function of N) of the sum \sum_{n=1}^N (-1)^{\floor{n x}} for various…
Fraenkel's Partition and Brown's Decomposition
Kevin O'Bryant
Denote the sequence ([ (n-x') / x ])_{n=1}^\infty by B(x, x'), a so-called Beatty sequence. Fraenkel's Partition Theorem gives necessary and sufficient conditions for B(x, x') and…
Continuous Ramsey Theory and Sidon Sets
Greg Martin, Kevin O'Bryant
A symmetric subset of the reals is one that remains invariant under some reflection x --> c-x. Given 0 < x < 1, there exists a real number D(x) with the following property: if 0 <…