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The existence of a class of Kirkman squares of index 2. (English) Zbl 0668.05016
A Kirkman square $$KS_ 3(v;1,2)$$ is a (v-1)$$\times (v-1)$$ array K with entries from a (v-1)-set V so that (1) each cell is empty of contains a 3-subset of V, (2) each element of V is exactly once in each row and column of K and (3) the collection of 3-subsets in K form a BIBD(v- 1,3,2).
The authors construct $$KS_ 3(v;1,2)$$ for all $$v\equiv 3(mod 12)$$. (Observe that Kirkman squares are a generalization of Room squares; a good survey of such generalizations is given by A. Rosa [Ann. Discrete Math. 8, 43-57 (1980; Zbl 0445.05026)].)
Reviewer: K.Heinrich

##### MSC:
 05B30 Other designs, configurations
##### Keywords:
balanced incomplete block design; Kirkman system; frame