34 citations · 268 across the 120 of their papers we have counts for
6 papers · 1 filter
Nets in groups, minimum length -adic representations, and minimal additive complements
Melvyn B. Nathanson
The number theoretic analogue of a net in metric geometry suggests new problems and results in combinatorial and additive number theory. For example, for a fixed integer g > 1, the…
Phase transitions in infinitely generated groups, and related problems in additive number theory
Melvyn B. Nathanson
Let A be an infinite set of generators for a group G, and let L_A(r) denote the number of elements of G whose word length with respect to A is exactly r. The purpose of this note i…
Desperately seeking mathematical truth
Melvyn B. Nathanson
This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.
Problems in Additive Number Theory, III: Thematic Seminars at the Centre de Recerca Matematica
Melvyn B. Nathanson
This is a survey of open problems in different parts of combinatorial and additive number theory. The paper is based on lectures at the Centre de Recerca Matematica in Barcelona on…
Supersequences, rearrangements of sequences, and the spectrum of bases in additive number theory
Melvyn B. Nathanson
The set A = {a_n} of nonnegative integers is an asymptotic basis of order h if every sufficiently large integer can be represented as the sum of h elements of A. If a_n ~ alpha n^h…
Linear forms and complementing sets of integers
Melvyn B. Nathanson
Let be a linear form with nonzero integer coefficients Let be an -tup…