Related papers: A new structure for difference matrices over abeli…
A linking system of difference sets is a collection of mutually related group difference sets, whose advantageous properties have been used to extend classical constructions of systems of linked symmetric designs. The central problems are…
A packing of partial difference sets is a collection of disjoint partial difference sets in a finite group $G$. This configuration has received considerable attention in design theory, finite geometry, coding theory, and graph theory over…
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…
We introduce the concept of linked systems of symmetric group divisible designs. The connection with association schemes is established, and as a consequence we obtain an upper bound on the number of symmetric group divisible designs which…
A dilatation structure on a metric space, arXiv:math/0608536v4, is a notion in between a group and a differential structure, accounting for the approximate self-similarity of the metric space. The basic objects of a dilatation structure are…
For nearly a century, mathematicians have been developing techniques for constructing abelian automorphism groups of combinatorial objects, and, conversely, constructing combinatorial objects from abelian groups. While abelian groups are a…
A dilatation structure is a concept in between a group and a differential structure. In this article we study fundamental properties of dilatation structures on metric spaces. This is a part of a series of papers which show that such a…
An imprimitive symmetric indecomposable association scheme of rank 5 is said to be Higmanian. A divisible design graph is a graph whose adjacency matrix is an incidence matrix of a symmetric divisible design. We establish conditions which…
We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with particular emphasis on the set D' comprised of differences between successive…
Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory and cryptography. In this paper, some new series…
Difference sets have been studied for more than 80 years. Techniques from algebraic number theory, group theory, finite geometry, and digital communications engineering have been used to establish constructive and nonexistence results. We…
We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel…
We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the…
We give a framework for generalizing LDPC code constructions that use Transversal Designs or related structures such as mutually orthogonal Latin squares. Our construction offers a broader range of code lengths and codes rates. Similar…
Cretan matrices are orthogonal matrices with elements $\leq 1$. These may have application in forming some new materials. There is a search for Cretan matrices, especially with high determinant, for all orders. These have been found by both…
Difference families are traditionally built using groups as their basis. This paper looks at what sort of generalised difference family constructions could be made, using the standard basis of translation and difference. The main result is…
We provide a method to construct $t$-designs from weighing matrices and association schemes. One instance of our method can produce a $3$-design from any (symmetric or skew-symmetric) conference matrix, thereby providing a partial answer to…
Difference triangle sets are useful in many practical problems of information transmission. This correspondence studies combinatorial and computational constructions for difference triangle sets having small scopes. Our algorithms have been…
A $(v, k, \lambda)$ symmetric design is said to have the symmetric difference property (SDP) if the symmetric difference of any three blocks is either a block or the complement of a block. Symmetric designs fulfilling this property have the…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…