On the existence of (v,7,1)-perfect Mendelsohn designs

On the existence of perfect Mendelsohn designs with k = 7 and A even

Let v, k and I be positive integers. A (v, k, A)-Mendelsohn design (briefly (v, k, A)-MD) is a pair (X, 3) where X is a v-set (of points) and !?8 is a collection of cyclically ordered k-subsets of X (called blocks) such that every ordered pair of points of X are consecutive in exactly il blocks of 3. A set of k distinct elements {a,, a-,, . . . , ak} is said to be cyclically ordered by a,Ca,C.‘...

Perfect Mendelsohn designs with block size six

The existence of ( v , 6 , λ ) - perfect Mendelsohn designs with λ > 1

The basic necessary conditions for the existence of a (v, k, λ)-perfect Mendelsohn design (briefly (v, k, λ)-PMD) are v ≥ k and λv(v− 1) ≡ 0 (mod k). These conditions are known to be sufficient in most cases, but certainly not in all. For k = 3, 4, 5, 7, very extensive investigations of (v, k, λ)-PMDs have resulted in some fairly conclusive results. However, for k = 6 the results have been far ...

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

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...