Delaney, Cathy, Gray, Brenton D., Gray, Ken, Maenhaut, Barbara M., Sharry, Martin J. and Street, Anne Penfold (1997) Pointwise defining sets and trade cores. Australasian Journal of Combinatorics, 1651-76.
A block design D = (V, B) is a set V of v elements together with a set B of b subsets of V called blocks, each containing exactly k elements, such that each element of V occurs in precisely r blocks, for some positive integers rand k. D is called a t-design if every t-subset of V occurs in exactly λt blocks, for some positive integer λt. Such a design D is described as a t-( v, k, λt) design. λ t-( v, k, λt) defining set has previously been defined as a set of blocks which is a subset of a unique t-(v, k, λt) design. A defining set is now more broadly defined to be a set of full and/or partial blocks which is contained in a unique t-( v, k, λt) design. It is a pointwise defining set if partial blocks are present. If only full blocks are present, it may be considered as either a pointwise or a blockwise defining set. The results presented here lead to useful tools for finding both pointwise defining sets of designs, and the relevant generalization of trades. Some examples are given to illustrate this.