On the possible orders of a basis for a finite cyclic group
Journal article, 2010

We prove a result concerning the possible orders of a basis for the cyclic group Z(n), namely: For each k is an element of N there exists a constant c(k) > 0 such that, for all n is an element of N, if A subset of Z(n) is a basis of order greater than n/k, then the order of A is within c(k) of n/l for some integer l is an element of [1, k]. The proof makes use of various results in additive number theory concerning the growth of sumsets. Additionally, exact results are summarized for the possible basis orders greater than n/4 and less than root n. An equivalent problem in graph theory is discussed, with applications.






P. Dukes

Peter Hegarty

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

S. Herke

Electronic Journal of Combinatorics

1097-1440 (ISSN) 1077-8926 (eISSN)

Vol. 17 1 #R79-

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Other Mathematics

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