RESOLVABLE MENDELSOHN DESIGNS AND FINITE FROBENIUS GROUPS

The existence of resolvable Mendelsohn designs RMD({3, s*}, v)

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...

Finite Groups, Designs and Codes

Introduction Terminology and notation Group Actions and Permutation Characters Method 1 References Finite Groups, Designs and Codes J Moori School of Mathematical Sciences, University of KwaZulu-Natal Pietermaritzburg 3209, South Africa ASI, Opatija, 31 May –11 June 2010 J Moori, ASI 2010, Opatija, Croatia Groups, Designs and Codes Abstract Introduction Terminology and notation Group Actions an...

Constructions of simple Mendelsohn designs

A Mendelsohn design M(k,v) is a pair (V,B) t where IV\=v and B is a set of cyclically ordered k-tuples of distinct elements of V, called blocks, such that every ordered pair of distinct elements of V belongs to exactly one block of B. A M( k, v) is called cyclic if it has an automorphism consisting of a single cycle of length v. The spectrum of existence of cyclic M(3,v)'s and M(4,v)'s is known...

Thickly-resolvable block designs

We show that the necessary divisibility conditions for the existence of a σ-resolvable BIBD(v, k, λ) are sufficient for large v. The key idea is to form an auxiliary graph based on an [r, k]-configuration with r = σ, and then edge-decompose the complete λ-fold graph K (λ) v into this graph. As a consequence, we initiate a similar existence theory for incomplete designs with index λ. ∗ Supported...