7 papers · 1 filter
Maximal Sidon Sets and Matroids
J. A. Dias da Silva, Melvyn B. Nathanson
Let X be a subset of an abelian group and a_1,...,a_h,a'_1,...,a'_h a sequence of 2h elements of X such that a_1 + ... + a_h = a'_1 + ... + a'_h. The set X is a Sidon set of order…
A new upper bound for finite additive bases
Sinan Gunturk, Melvyn B. Nathanson
Let n(2,k) denote the largest integer n for which there exists a set A of k nonnegative integers such that the sumset 2A contains {0,1,2,...,n-1}. A classical problem in additive n…
The inverse problem for representation functions of additive bases
Melvyn B. Nathanson
Let A be a set of integers. For every integer n, let r_{A,2}(n) denote the number of representations of n in the form n = a_1 + a_2, where a_1 and a_2 are in A and a_1 \leq a_2. Th…
Additive number theory and the ring of quantum integers
Melvyn B. Nathanson
Let and be positive integers. For the quantum integer there is a natural polynomial addition such that and…
N-graphs, modular Sidon and sum-free sets, and partition identities
Melvyn B. Nathanson
Using a new graphical representation for partitions, the author obtains a family of partition identities associated with partitions into distinct parts of an arithmetic progression…
On Erdos's elementary method in the asymptotic theory of partitions
Melvyn B. Nathanson
Let m be a positive integer, and let A be the set of all positive integers that belong to a union of r distinct congruence classes modulo m. We assume that the elements of A are re…