Perfect Mendelsohn designs with block size six

Perfect Mendelsohn designs with block size six

Self-converse Mendelsohn designs with odd block size

A Mendelsohn design .M D(v, k,).) is a pair (X, B), where X is a vset together with a collection B of ordered k-tuples from X such that each ordered pair from X is contained in exactly ). k-tuples of B. An M D(v, k,).) is said to be self-converse, denoted by SC!'vf D( v, k,).) = (X,B,/), if there is an isomorphism / from (X, B) to (X,B), where B-1 {(Xk,:r:k-l, ... ,X2,Xl); (Xl,,,,,Xk) E B}. The...

Self-converse Mendelsohn designs with block size 6q

A Mendelsohn design lv! D( v, k, A) is a pair (X, B) where X is a v-set together with a collection B of cyclic k-tuples from X such that each ordered pair from X is contained in exactly A cyclic k-tuples of B. An M D(v, k, A) is said to be self-converse, denoted by SC1\ID(v,k,A) = (X,B,f), if there is an isomorphism f from (X, B) to (X, B-1), where B1 = {(:Ek,:r:k-l, ""X2,Xl!: (:1:1, ""Xk! E B}...

Halving block designs with block size four

B) is said to have the Size Four property if the blocks in B can be partitioned into two isomorphic sets. In this paper we construct block with four with the property, thus the exception of 6 A. Rosa [4]).

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 ...