A095025 -id:A095025 - cp's OEIS frontend

A095029 An example of a (v,k,lambda)=(21,5,1) cyclic difference set.

3, 6, 7, 12, 14

Offset: 1

Hugo Pfoertner, May 27 2004

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 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)

			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

Leonard D. Baumert and 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.

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).

A095047 An example of a (v,k,lambda)=(107,53,26) cyclic difference set.

Original entry on oeis.org

1, 3, 4, 9, 10, 11, 12, 13, 14, 16, 19, 23, 25, 27, 29, 30, 33, 34, 35, 36, 37, 39, 40, 41, 42, 44, 47, 48, 49, 52, 53, 56, 57, 61, 62, 64, 69, 75, 76, 79, 81, 83, 85, 86, 87, 89, 90, 92, 99, 100, 101, 102, 105

Offset: 1

Hugo Pfoertner, May 27 2004

See A095029. This is an example of a difference set that produces a large number of different representations.

Dan Gordon, List of Cyclic Difference Sets, (2003).
Dan Gordon, Difference Sets, searchable database.

Cf. A095025 (number of cyclic difference sets with n elements), A095029-A095046 (more examples of cyclic difference sets with k=5..20).

A095028 An example of a (v,k,lambda)=(11,5,2) cyclic difference set.

Original entry on oeis.org

1, 3, 4, 5, 9

Offset: 1

Hugo Pfoertner, Jun 02 2004

See A095029.

			Using the numbers {1 3 4 5 9}, every number in the range 1..10 can be written as a difference modulo 11 in two different ways:
1=4-3=5-4, 2=3-1=5-3, 3=4-1=(1-9) mod 11, 4=5-1=9-5, 5=9-4=(3-9) mod 11,
6=9-2=(4-9) mod 11, 7=(1-5) mod 11=(5-9) mod 11, 8=9-1=(1-4) mod 11,
9=(1-3) mod 11=(3-5) mod 11, 10=(3-4) mod 11=(4-5) mod 11.

Dan Gordon, List of Cyclic Difference Sets, (2003).

Cf. A095025 number of cyclic difference sets with n elements, A095029 .. A095047 more examples of cyclic difference set with k=5..53.

A095030 An example of a (v,k,lambda)=(31,6,1) cyclic difference set.

Original entry on oeis.org

1, 5, 11, 24, 25, 27

Offset: 1

Hugo Pfoertner, May 27 2004

See A095029.

Dan Gordon, List of Cyclic Difference Sets, (2003).
Dan Gordon, Difference Sets, searchable database.

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).

A095032 An example of a (v,k,lambda)=(57,8,1) cyclic difference set.

Original entry on oeis.org

0, 1, 6, 15, 22, 26, 45, 55

Offset: 1

Hugo Pfoertner, May 27 2004

See A095029.

Dan Gordon, List of Cyclic Difference Sets, (2003).
Dan Gordon, Difference Sets, searchable database.

Cf. A095025 (number of cyclic difference sets with n elements), A095029-A095047 (more examples of cyclic difference sets with k=5..20), A000961 (prime powers).

A095035 An example of a (v,k,lambda)=(73,9,1) cyclic difference set.

Original entry on oeis.org

0, 1, 12, 20, 26, 30, 33, 35, 57

Offset: 1

Hugo Pfoertner, May 27 2004

See A095029.

Dan Gordon, List of Cyclic Difference Sets, (2003).
Dan Gordon, Difference Sets, searchable database.

Cf. A095025 (number of cyclic difference sets with n elements), A095029-A095047 (more examples of cyclic difference sets with k=5..20), A000961 (prime powers).

A095036 An example of a (v,k,lambda)=(91,10,1) cyclic difference set.

Original entry on oeis.org

0, 2, 6, 7, 18, 21, 31, 54, 63, 71

Offset: 1

Hugo Pfoertner, May 27 2004

See A095029.

Dan Gordon, List of Cyclic Difference Sets, (2003).
Dan Gordon, Difference Sets, searchable database.

Cf. A095025 (number of cyclic difference sets with n elements), A095029-A095047 (more examples of cyclic difference sets with k=5..20), A000961 (prime powers).

A095038 An example of a (v,k,lambda)=(133,12,1) cyclic difference set.

Original entry on oeis.org

1, 10, 11, 13, 27, 31, 68, 75, 83, 110, 115, 121

Offset: 1

Hugo Pfoertner, May 27 2004

See A095029.

Dan Gordon, List of Cyclic Difference Sets, (2003).
Dan Gordon, Difference Sets, searchable database.

Cf. A095025 (number of cyclic difference sets with n elements), A095029-A095047 (more examples of cyclic difference sets with k=5..20), A000961 (prime powers).

A095040 An example of a (v,k,lambda)=(183,14,1) cyclic difference set.

Original entry on oeis.org

1, 13, 20, 21, 23, 44, 61, 72, 77, 86, 90, 116, 122, 169

Offset: 1

Hugo Pfoertner, May 27 2004

See A095029.

Dan Gordon, List of Cyclic Difference Sets, (2003).
Dan Gordon, Difference Sets, searchable database.

Cf. A095025 (number of cyclic difference sets with n elements), A095029-A095047 (more examples of cyclic difference sets with k=5..20), A000961 (prime powers).

A095041 One of two (v,k,lambda)=(31,15,7) cyclic difference sets. The other one is A095042.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 12, 15, 16, 17, 23, 24, 27, 29, 30

Offset: 1

Hugo Pfoertner, May 27 2004

See A095029.

Dan Gordon, List of Cyclic Difference Sets, (2003).
Dan Gordon, Difference Sets, searchable database.

Cf. A095025 (number of cyclic difference sets with n elements), A095029-A095047 (more examples of cyclic difference sets with k=5..20).

cp's OEIS Frontend

A095029 An example of a (v,k,lambda)=(21,5,1) cyclic difference set.

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A095047 An example of a (v,k,lambda)=(107,53,26) cyclic difference set.

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A095028 An example of a (v,k,lambda)=(11,5,2) cyclic difference set.

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A095030 An example of a (v,k,lambda)=(31,6,1) cyclic difference set.

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A095032 An example of a (v,k,lambda)=(57,8,1) cyclic difference set.

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A095035 An example of a (v,k,lambda)=(73,9,1) cyclic difference set.

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A095036 An example of a (v,k,lambda)=(91,10,1) cyclic difference set.

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A095038 An example of a (v,k,lambda)=(133,12,1) cyclic difference set.

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A095040 An example of a (v,k,lambda)=(183,14,1) cyclic difference set.

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A095041 One of two (v,k,lambda)=(31,15,7) cyclic difference sets. The other one is A095042.

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