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On the possible ord...
On the possible orders of a basis for a finite cyclic group
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Dukes, P. (author)
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- Hegarty, Peter, 1971 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg
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Herke, S. (author)
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(creator_code:org_t)
- 2010
- 2010
- English.
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In: Electronic Journal of Combinatorics. - 1077-8926 .- 1097-1440. ; 17:1
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Abstract
Subject headings
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik -- Annan matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Other Mathematics (hsv//eng)
Keyword
- Abelian-groups
- Matrices
- Exponent
- Theorem
- Abelian-groups
Publication and Content Type
- ref (subject category)
- art (subject category)
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