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Discrete Mathematics and Combinatorics Commons™

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1993

Articles 1 - 7 of 7

Full-Text Articles in Discrete Mathematics and Combinatorics

New Constructions Of Menon Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Surinder K. Sehgal Nov 1993

New Constructions Of Menon Difference Sets, K. T. Arasu, James A. Davis, Jonathan Jedwab, Surinder K. Sehgal

Department of Math & Statistics Faculty Publications

Menon difference sets have parameters (4N2, 2N2 − N, N2 − N). These have been constructed for N = 2a3b, 0 ⩽ a,b, but the only known constructions in abelian groups require that the Sylow 3-subgroup be elementary abelian (there are some nonabelian examples). This paper provides a construction of difference sets in higher exponent groups, and this provides new examples of perfect binary arrays.

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A Note On New Semi-Regular Divisible Difference Sets, James A. Davis, Jonathan Jedwab Oct 1993

A Note On New Semi-Regular Divisible Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

We give a construction for new families of semi-regular divisible difference sets. The construction is a variation of McFarland's scheme [5] tor noncyclic difference sets.

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Rely To "Comment On 'Nonexistence Of Certain Perfect Binary Arrays' And 'Nonexistence Of Perfect Binary Arrays'", Jonathan Jedwab, James A. Davis May 1993

Rely To "Comment On 'Nonexistence Of Certain Perfect Binary Arrays' And 'Nonexistence Of Perfect Binary Arrays'", Jonathan Jedwab, James A. Davis

Department of Math & Statistics Faculty Publications

Yang's comment [C] is based on a lemma which claims to construct an s0 x s1 x s2 x ... x s, perfect binary array (PBA) from an s0s1 x s2 x ... x sr PBA.

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Hypergraph Representations And Orders Of Cwatsets, Julie Kerr Mar 1993

Hypergraph Representations And Orders Of Cwatsets, Julie Kerr

Mathematical Sciences Technical Reports (MSTR)

We determine upper bounds on the order of cwatsets of odd order.

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Optimal Leapfrogging, Joel Auslander, Arthur T. Benjamin, Daniel S. Wilkerson Feb 1993

Optimal Leapfrogging, Joel Auslander, Arthur T. Benjamin, Daniel S. Wilkerson

All HMC Faculty Publications and Research

No abstract provided in this article.

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Nonexistence Of Certain Perfect Binary Arrays, Jonathan Jedwab, James A. Davis Jan 1993

Nonexistence Of Certain Perfect Binary Arrays, Jonathan Jedwab, James A. Davis

Department of Math & Statistics Faculty Publications

A perfect binary array (PBA) is an r-dimensional matrix with elements ±I such that all out-of-phase periodic autocorrelation coefficients are zero. The two smallest sizes for which the existence of a PBA is undecided, 2 x 2 x 3 x 3 x 9 and 4 x 3 x 3 x 9, are ruled out using computer search and a combinatorial argument.

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A Summary Of Menon Difference Sets, James A. Davis, Jonathan Jedwab Jan 1993

A Summary Of Menon Difference Sets, James A. Davis, Jonathan Jedwab

Department of Math & Statistics Faculty Publications

A (v, k, λ) difference set is a k-element subset D of a group G of order v for which the multiset {d1d2-1 : d1,d2 ∈ D, d1 ≠ d2} contains each nonidentity element of G exactly λ times. A difference set is called abelian, nonabelian or cyclic if the underlying group is. Difference sets a.re important in design theory because they a.re equivalent to symmetric (v, k, λ) designs with a regular automorphism group. Abelian difference sets arise naturally in …

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