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A class of resolvable pairwise balanced designs. (English) Zbl 0611.05008
Combinatorics, graph theory, and computing, Proc. 17th Southeast. Conf., Boca Raton/Fl. 1986, Congr. Numerantium 55, 211-220 (1986).
[For the entire collection see Zbl 0608.00004.]
A restricted resolvable pairwise balanced design $$R_{\ell}RP(p,k)$$ is a pairwise balanced design of index 1 on p treatments with all blocks of size $$\ell$$ or $$\ell +1$$, such that blocks may be resolved into k parallel classes. We indicate why such designs arise and prove the existence of $$R_ 2RP(p,k)$$ whenever $$p\equiv 0$$ (mod 6) and p/2$$\leq k\leq p-1$$, with the exceptions $$(p,k)=(6,3)$$ or (12,6). We also give some constructions yielding several infinite families of $$R_ 2RP(p,k)$$ for $$p\not\equiv 0$$ (mod 6).

##### MSC:
 05B05 Combinatorial aspects of block designs
##### Keywords:
restricted resolvable pairwise balanced design