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Class-uniformly resolvable pairwise balanced designs with block size two and three. (English) Zbl 0749.05011
A pairwise balanced design (PBD) is a pair \((X,B)\), where \(X\) is a set of points and \(B\) is a collection of subsets of \(X\) called blocks, such that each pair of points is contained in exactly one block. A parallel class of blocks in a PBD is a subset of \(B\) which partitions the point set, and a PBD is called resolveable if \(B\) admits a partition \(B_ 1,\ldots,B_ k\) into parallel classes. A class-uniformly resolvable pairwise balanced design \(\text{CURD}(K;p,r)\) is a PBD on \(p\) points, with block sizes from the set \(K\), whose block set can be resolved into \(r\) parallel classes, each parallel class containing a fixed number \(a_ k\) of blocks of size \(k\in K\). The authors indicate why such designs arise, and give some examples for \(K=\{2,3\}\).

MSC:
05B05 Combinatorial aspects of block designs
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