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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
##### Keywords:
pairwise balanced designs
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##### References:
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