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math.NT2000
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…
math.NT2000
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…
math.NT2000
Asymptotic density and the asymptotics of partition functions
Melvyn B. Nathanson
Let A be a set of positive integers with gcd(A) = 1, and let p_A(n) be the partition function of A. Let c = π\sqrt(2/3). Let α> 0. It is proved that log p_A(n) ~ c\sqrt(αn) if and…