Anne Penfold Street

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The existence of blocking sets in (v, {2, 4}, 1)-designs is examined. We show that for v ≡ 0, 3, 5, 6, 7, 8, 9, 11 (mod 12), blocking sets cannot exist. We prove that for each v ≡ 1, 2, 4 (mod 12) there is a (v, {2, 4}, 1)-design with a blocking set with three possible exceptions. The case v ≡ 10 (mod 12) is still open; we consider the first four values of(More)
In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges. 1 Background information In any combinatorial connguration it is possible to identify a subset which uniquely determines the structure of(More)
The concept of defining set has been studied in block designs and, under the name critical sets, in Latin squares and Room squares. Here we study defining sets for directed designs. A t-(v, k,'x) directed design (DD) is a pair (V, B), where V is a v-set and B is a collection of ordered blocks (or k-tuples of V), for which each t-tuple of V appears in(More)