Abstract:
We prove imbedding theorems for block designs balanced with respect to pairs, and with the aid of these theorems we establish the existence of $(v,k,\lambda)$-resolvable BIB block designs with parameters $v,k,\lambda$ such that $\lambda=k-1$ [and also such that $\lambda=(k-l)/2$ if $k$ is odd], $k\mid(p-1)$ for each prime divisor $p$ of the number $v/k$; we also establish an imbedding theorem for Kirkman triple systems.
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