Published 1997 by Hewlett-Packard Laboratories, Technical Publications Dept. in Palo Alto, Calif .
Written in EnglishRead online
|Statement||James A. Davis.|
|Series||HP Laboratories technical report -- HPL-96-34.|
|Contributions||Jedwab, Jonathan., Mowbray, Miranda., Hewlett-Packard Laboratories.|
|The Physical Object|
|Pagination||16 p. ;|
|Number of Pages||16|
Download New families of semi-regular relative difference sets
We recursively construct a new family New families of semi-regular relative difference sets book (26d+4, 8, 26d+4, 26d+1) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup U.
New Families of Semi-Regular Relative Difference Sets. We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2. No such RDSs were previously known.
We use examples from the first construction to produce semi-regular RDSs in groups whose order can contain more than two distinct prime by: CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We give two constructions for semi-regular relative difference sets (RDSs) in groups whose order is not a prime power, where the order u of the forbidden subgroup is greater than 2.
No such RDSs were previously known. We use examples from the first construction to produce semi-regular RDSs in groups whose. New families of semi-regular relative difference sets.
By J. Davis, J Jedwab and Bristol (United Kingdom) Hewlett-Packard Laboratories. Abstract. SIGLEAvailable from British Library Document Supply Centre-DSC(HPL(rev.1)) / BLDSC. We recursively construct a new family of (26d+4, 8, 26d+4, 26d+1) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup U.
The initial case d = 0 of the recursion comprises examples of (16, 8, 16, 2) relative difference sets for four distinct pairs (G, U). New families of semi-regularrelative difference sets James A. Davis; Mathematics and Computer Science, University of Richmond, VirginiaU.S.A.
In this note, we shall construct a new family of relative difference sets by generalizing a result of Spence . THEOREM. Let q be a prime power, d a positive integer, N = EA(gd + 1) the elementary abelian group of order qd + 1, and K any group of order " The author thanks the University of Waterloo for its hospitality during the time of this.
Abstract. We recursively construct a new family of (2 6d+4, 8, 2 6d+4, 2 6d+1) semi-regular relative difference sets in abelian groups G relative to an elementary abelian subgroup initial case d = 0 of the recursion comprises examples of (16, 8, 16, 2) relative difference sets for.
building sets, characters We recursively construct a new family of (26d+4, 8, 26d+4, 26d+1) semi-regular relative difference sets in abelian groupsG relative to an elementary abelian subgroupU.
The initial case d = 0 of the recursion comprises examples New families of semi-regular relative difference sets book (16,8,16,2) relative difference sets for four distinct pairs (G, U). As nouns the difference between family and relative is that family is (lb) a group of people who are closely related to one another (by blood or marriage); for example, a set of parents and their children; an immediate family while relative is someone in the same family; someone connected by blood, marriage, or adoption.
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In fact one difference set was omitted. Thus the above construction gives three inequivalent (35, 15, 6) difference sets in Zs x ZF and four inequivalent (36, 15, 6) difference sets in Z;3 x_ Z, x Z, which are the only ones possible.
REFERENCES 1. MCFARLAND, A family of difference sets in non-cyclic groups, J. Combinatorial Theory Lingadapted from UMass LingPartee lecture notes March 1, p.
4 Set Theory Subsets A set A is a subset of a set B iff every element of A is also an element of a relation between sets is denoted by A ⊆ A ⊆ B and A ≠ B we call A a proper subset of B and write A ⊂ B.
(Caution: sometimes ⊂ is used the way we are using ⊆.). Family groups with this structure can also be called a conjugal family because these families, headed by a married couple, are the family of procreation.
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No: theorem (parts (e) and (f)) concerns the intersection or union of two sets only. This can be extended easily to any intersection or union of a finite number of sets, though even this modest extension does require separate proof. The real problem is with intersections or unions of an infinite number of sets.
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