Inspired by some intriguing examples, we study uniform association schemes and uniform
coherent configurations, including cometric Q-antipodal association schemes. After a review …

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 …

In the present paper, we study relative difference sets (RDSs) and linked systems of them. It
is shown that a closed linked system of RDSs is always graded by a group. Based on this …

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 …

A linked system of symmetric designs (LSSD) is a w-partite graph (w⩾ 2) where the
incidence between any two parts corresponds to a symmetric design and the designs arising …

One may think of a $ d $-class association scheme as a $(d+ 1) $-dimensional matrix
algebra over $\mathbb {R} $ closed under Schur products. In this context, an imprimitive …

In this paper, when the order of $\theta $ is even, we prove that there exists no central
difference sets in $ A_2 (m,\theta) $ and establish some non-existence results of central …

Collections of difference sets called linking systems have been used to construct new
families of linked systems of symmetric designs. In this paper, we define relative and almost …

A difference matrix over a group is a discrete structure that is intimately related to many other
combinatorial designs, including mutually orthogonal Latin squares …

Inthispaper, weconsidertheproblemoflinkingsystemsofdif… well as variations. We review
recent results on the subject, give new constructions of linked relative difference sets and …