منابع مشابه
A Brief Survey of Difference Sets, Partial Difference Sets, and Relative Difference Sets
Difference sets, partial difference sets, and relative difference sets are algebraic structures with combinatorial applications. The purpose of this paper is to give the reader definitions and basic examples of these sets, as well describe their connections to some other well-known combinatorial objects. We will conclude with some examples that illustrate how character theory can be used to pro...
متن کاملConstructions of Partial Difference Sets and Relative Difference Sets on /7-groups
By using some finite local rings, we construct some new partial difference sets and relative difference sets on ^-groups where p is any prime. When p = 2, some of the partial difference sets constructed are reversible difference sets which include Dillon's difference sets.
متن کاملRelative Difference Sets Partitioned by Cosets
We explore classical (relative) difference sets intersected with the cosets of a subgroup of small index. The intersection sizes are governed by quadratic Diophantine equations. Developing the intersections in the subgroup yields an interesting class of group divisible designs. From this and the Bose-Shrikhande-Parker construction, we obtain some new sets of mutually orthogonal latin squares. W...
متن کاملOn non-Abelian group difference sets
This paper is motivated by R. H. Bruck’s paper[3], in which he proved that the existence of cyclic projective plane of order n ≡ 1 (mod 3) implies that of a non-planar difference set of the same order by proving that such a cyclic projective plane admits a regular non-Abelian automorphism group using n as a multiplier. In this paper we will discuss in detail the possibility of using multipliers...
متن کاملOn non-existence of some difference sets
Eric Lander conjectured that if G is an abelian group of order v containing a difference set of order n and p is a prime dividing v and n, then the Sylow p-subgroup of G cannot be cyclic. This paper verifies a version of this conjecture for k < 6500. A special case of this version is the non-existence of Menon-Hadamard-McFarland difference sets in 2-groups. We also give an algorithm that easily...
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ژورنال
عنوان ژورنال: Hokkaido Mathematical Journal
سال: 2008
ISSN: 0385-4035
DOI: 10.14492/hokmj/1253539528