

A095029


The (v,k,lambda)=(21,5,1) cyclic difference set.


21




OFFSET

1,1


COMMENTS

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,...,v1} can each be represented as a difference (d_id_j) modulo v in exactly lambda different ways. Difference sets with lambda=1 (planar difference sets) have group order n=k1. 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)


LINKS

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, arXiv:math/0304502 [math.CO], 30 Apr 2003.
Dan Gordon, List of Cyclic Difference Sets, (2003).
Dan Gordon, Difference Sets, searchable database.


EXAMPLE

Representation of {1,...,20}: 1=76, 2=1412, 3=63, 4=73, 5=127, 6=126, 7=147, 8=146, 9=123, 10=21+314, 11=143, 12=21+312, 13=21+614, 14=21+714, 15=21+612, 16=21+712, 17=21+37, 18=21+36, 19=21+1214, 20=21+67.  Hugo Pfoertner, Aug 13 2011


CROSSREFS

Cf. A095025 (number of cyclic difference sets with n elements), A095029A095047 (more examples of cyclic difference set with k=5..20), A000961 (prime powers).
Sequence in context: A333794 A182181 A138038 * A028792 A325804 A144795
Adjacent sequences: A095026 A095027 A095028 * A095030 A095031 A095032


KEYWORD

fini,full,nonn


AUTHOR

Hugo Pfoertner, May 27 2004


STATUS

approved



