Affiliation:
1. Department of Mathematics, Lehman College (CUNY), Bronx, NY 10648, USA
Abstract
The number theoretic analog of a net in metric geometry suggests new problems and results in combinatorial and additive number theory. For example, for a fixed integer g ≥ 2, the study of h-nets in the additive group of integers with respect to the generating set Ag = {0} ∪ {± gi : i = 0, 1, 2, …} requires a knowledge of the word lengths of integers with respect to Ag. A g-adic representation of an integer is described that algorithmically produces a representation of shortest length. Additive complements and additive asymptotic complements are also discussed, together with their associated minimality problems.
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
19 articles.
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