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A095029
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The (v,k,lambda)=(21,5,1) cyclic difference set.
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21
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OFFSET
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1,1
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COMMENTS
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A (v,k,lambda) cyclic difference set is a subset D={d_1,d_2,...,d_k} of the integers modulo v such that {1,2,...,v-1} can each be represented as a difference (d_i-d_j) modulo v in exactly lambda different ways. Difference sets with lambda=1 (planar difference sets) have group order n=k-1. The Prime Power Conjecture states that all Abelian planar difference sets have order n a prime power. It is known that no cyclic planar difference sets of nonprime power order n exist with n < 2*10^9 (see Baumert, Gordon link)
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LINKS
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Table of n, a(n) for n=1..5.
Leonard D. Baumert, Daniel M. Gordon, On the existence of cyclic difference sets with small parameters.
Dan Gordon, List of Cyclic Difference Sets
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EXAMPLE
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Representation of {1,...,20}: 1=7-6, 2=14-12, 3=6-3, 4=7-3, 5=12-7, 6=12-6, 7=14-7, 8=14-6, 9=12-3, 10=21+3-14, 11=14-3, 12=21+3-12, 13=21+6-14, 14=21+7-14, 15=21+6-12, 16=21+7-12, 17=21+3-7, 18=21+3-6, 19=21+12-14, 20=21+6-7. [Hugo Pfoertner, Aug 13 2011]
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CROSSREFS
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Cf. A095025 number of cyclic difference sets with n elements, A095029-A095047 more examples of cyclic difference set with k=5..20, A000961 prime powers.
Sequence in context: A038591 A182181 A138038 * A028792 A144795 A077459
Adjacent sequences: A095026 A095027 A095028 * A095030 A095031 A095032
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KEYWORD
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fini,full,nonn
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AUTHOR
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Hugo Pfoertner, May 27 2004
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STATUS
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approved
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