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 Mat. Zametki: Year: Volume: Issue: Page: Find

 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 $\lambda=(k-1)/2$

Full text: PDF file (696 kB)

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}