Complete Sets of Disjoint Difference Families and their Applications
نویسندگان
چکیده
Let G be an abelian group. A collection of (G, k, λ) disjoint difference families, {F0,F1, · · · ,Fs−1}, is a complete set of disjoint difference families if ∪0≤i≤s−1∪B∈FiB form a partition of G− {0}. In this paper, several construction methods are provided for complete sets of disjoint difference families. Applications to one-factorizations of complete graphs and to cyclically resolvable cyclic Steiner triple systems are also described. Short running title: Difference families.
منابع مشابه
Disjoint difference families and their applications
Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of difference families and the variations in priorities in constructions. We propose a definition of disjoint difference families that encompasses these variations and...
متن کاملLimits and colimits in the category of pre-directed complete pre-ordered sets
In this paper, some categorical properties of the category { Pre-Dcpo} of all pre-dcpos; pre-ordered sets which are also pre-directed complete, with pre-continuous maps between them is considered. In particular, we characterize products and coproducts in this category. Furthermore, we show that this category is neither complete nor cocomplete. Also, epimorphisms and monomorphisms in {Pre-Dcpo} ...
متن کاملSix Constructions of Difference Families
In this paper, six constructions of difference families are presented. These constructions make use of difference sets, almost difference sets and disjoint difference families, and give new point of views of relationships among these combinatorial objects. Most of the constructions work for all finite groups. Though these constructions look simple, they produce many difference families with new...
متن کاملGenerating Edge-disjoint Sets of Quadruples in Parallel
Tightening interatomic distance bounds, obtained from NMR experiments, is a critical step in solving the molecular conformation problem. Tetrangle inequality (resulting from the Cayley-Menger determinant for the 3D embedding) is applied to quadruples of atoms in order to tighten the distance bounds. Complete graph Kn is used to model an n-atom molecule, where the nodes represent the atoms. Only...
متن کاملThe triples of geometric permutations for families of disjoint translates
A line meeting a family of pairwise disjoint convex sets induces two permutations of the sets. This pair of permutations is called a geometric permutation. We characterize the possible triples of geometric permutations for a family of disjoint translates in the plane. Together with earlier studies of geometric permutations this provides a complete characterization of realizable geometric permut...
متن کامل