Semiregular group divisible designs with dual properties

Semiregular group divisible designs whose duals are semiregular

ABSTRAC"T A construction method for semiregular group divisible designs is given. This method can be applied to yield many classes of (in general, non-symmetric) semiregular group divisible designs whose duals are semiregular group divisible. In particular, the method can be used to construct many classes of transversal designs whose duals are serniregular group divisible designs, but not trans...

Divisible designs with dual translation group

Many different divisible designs are already known. Some of them possess remarkable automorphism groups, so called dual translation groups. The existence of such an automorphism group enables us to characterize its associated divisible design as being isomorphic to a substructure of a finite affine space. AMS Classification: 05B05, 05B30, 20B25, 51N10

Resolvable Group Divisible Designs with Large Groups

We prove that the necessary divisibility conditions are sufficient for the existence of resolvable group divisible designs with a fixed number of sufficiently large groups. Our method combines an application of the Rees product construction with a streamlined recursion based on incomplete transversal designs. With similar techniques, we also obtain new results on decompositions of complete mult...

Construction of Group Divisible Designs

Divisible designs from twisted dual numbers

The generalized chain geometry over the local ring K(ε;σ) of twisted dual numbers, where K is a finite field, is interpreted as a divisible design obtained from an imprimitive group action. Its combinatorial properties as well as a geometric model in 4-space are investigated. Mathematics Subject Classification (2000): 51E05, 51B15, 51E20, 51E25, 51A45.