Reversible (m, n, k, λ1,λ2)-abelian divisible difference sets with k - λ1 nonsquare

Group divisible designs GDD(n, n, n, 1; λ1, λ2)

We give a complete solution for the existence problem of group divisible designs (or PBIBDs) with blocks of size k = 3, four groups of size (n, n, n, 1), and any two indices (λ1, λ2). Moreover, we introduce a construction of infinitely many group divisible designs with t groups of size n and one group of size 1. The construction technique utilizes our main result, together with some other known...

State Dependent M/M/C/K/N Machining System with Mixed Spares and Removable Repairmen

On the Rational Recursive Sequence X_{N+1}=ƔX_{N-K}+(AX_N+BX_{N-K})⁄(CX_N-DX_{N-K})

The $(n,m,k,\lambda)$-Strong External Difference Family with $m \geq 5$ Exists

Abstract The notion of strong external difference family (SEDF) in a finite abelian group (G,+) is raised by M. B. Paterson and D. R. Stinson [5] in 2016 and motivated by its application in communication theory to construct R-optimal regular algebraic manipulation detection code. A series of (n,m, k, λ)-SEDF’s have been constructed in [5, 4, 2, 1] with m = 2. In this note we present an example ...

New semiregular divisible difference sets

We modify and generalize the construction by McFarland (1973) in two different ways to construct new semiregular divisible difference sets (DDSs) with 21 ~ 0. The parameters of the DDS fall into a family of parameters found in Jungnickel (1982), where his construction is for divisible designs. The final section uses the idea of a K-matrix to find DDSs with a nonelementary abelian forbidden subg...