Self-converse Mendelsohn designs with block size 6q

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...

Perfect Mendelsohn designs with block size six

Note on the parameters of balanced designs

In discussing block designs we use the usual notations and terminology of the combinatorialliterature (see, for example, [1], [2]) "balance" will always mean pairwise balance and blocks do not contain repeated elements. It is well-known that a balanced design need not have constant block-size or constant replication number. However, it is easy to show ([2, p.22J). that in any balanced design wi...

Note on parameters of balanced ternary designs

Conditions under which constant block size implies constant replication number and vice versa are established for balanced ternary designs. This note is motivated by a note of almost the identical title of W. D. Wallis [2]. In a balanced binary design with constant block size, the replication number must be constant, but the converse is not true. Wallis [2] proved the following partial converse...

On generalised t-designs and their parameters

Recently, P.J. Cameron studied a class of block designs which generalises the classes of t-designs, α-resolved 2-designs, orthogonal arrays, and other classes of combinatorial designs. In fact, Cameron’s generalisation of t-designs (when there are no repeated blocks) is a special case of the “poset t-designs” in product association schemes studied ten years earlier by W.J. Martin, who further s...