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 Mat. Zametki, 1977, Volume 21, Issue 5, Pages 707–715 (Mi mz8001)

A recursive method of construction of resolvable $BIB$-designs

B. T. Rumov

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: A theorem is proved that every resolvable $BIB$-design $(v,k,\lambda)$ with $\lambda=k-1$ and the parameters $v$ and $k$ such that there exists a set of $k-1$ pairwise orthogonal Latin squares of order $v$ can be embedded in a resolvable $BIB$-design $(k+1)v,k,k-1)$. An analogous theorem is established for the class of arbitrary $BIB$-designs. As a consequence is deduced the existence of resolvable $BIB$-designs $(v,k,\lambda)$ with $\lambda=k-1$ and $(v,k,\lambda)$ with $\lambda=(k-1)/2$

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English version:
Mathematical Notes, 1977, 21:5, 395–399

Bibliographic databases:

UDC: 519.1

Citation: B. T. Rumov, “A recursive method of construction of resolvable $BIB$-designs”, Mat. Zametki, 21:5 (1977), 707–715; Math. Notes, 21:5 (1977), 395–399

Citation in format AMSBIB
\Bibitem{Rum77} \by B.~T.~Rumov \paper A~recursive method of construction of resolvable $BIB$-designs \jour Mat. Zametki \yr 1977 \vol 21 \issue 5 \pages 707--715 \mathnet{http://mi.mathnet.ru/mz8001} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=447007} \zmath{https://zbmath.org/?q=an:0398.05005|0391.05004} \transl \jour Math. Notes \yr 1977 \vol 21 \issue 5 \pages 395--399 \crossref{https://doi.org/10.1007/BF01788237}