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On the possible orders of a basis for a finite cyclic group

P. Dukes ; Peter Hegarty (Institutionen för matematiska vetenskaper, matematik) ; S. Herke
Electronic Journal of Combinatorics (1077-8926). Vol. 17 (2010), 1, p. #R79.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Abelian-groups, Matrices, Exponent, Theorem



Denna post skapades 2010-06-17. Senast ändrad 2012-01-25.
CPL Pubid: 122921

 

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Institutionen för matematiska vetenskaper, matematik (2005-2016)

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Annan matematik

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