Incomplete perfect Mendelsohn designs with block size four

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]).

Balanced incomplete block designs with block size~9: Part III

The necessary conditions for the existence of a balanced incomplete block design on v points, with index λ and block size k, are that: λ(v − 1) ≡ 0 mod (k − 1) λv(v − 1) ≡ 0 mod k(k − 1) Earlier work has studied k = 9 with λ ∈ {1, 2, 3, 4, 6, 8, 9, 12}. In this article we show that the necessary conditions are sufficient for λ = 9 and every other λ not previously studied.