On the spectrum of simple \(T(2,3,v)\) trades. (English) Zbl 1147.05018
A \(T(t,k,v)\)-trade \((V,T^+,T^-)\) is a triple in which \(V\) is a \(v\)-set, and \(T^+\) and \(T^-\) are disjoint collections of \(k\)-subsets (blocks) of \(V\), with the property that every \(t\)-subset of \(V\) appears equally often in the blocks of \(T^+\) and of \(T^-\). Its foundation is the set of elements appearing in at least one block of \(T^+\) (and hence also of \(T^-\). Its volume is the number of blocks in \(T^+\). This paper determines the spectrum of sizes of volumes of all \(T(2,3,v)\)-trades whose foundation has even size.
Reviewer: Charles J. Colbourn (Tempe)
Keywords:
trade; balanced incomplete block design; foundation of a triple; volume of a triple; foundation of a trade; volume of a tradeReferences:
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