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

 Mat. Zametki, 1976, Volume 19, Issue 4, Pages 623–634 (Mi mz7782)

The existence of some resolvable block designs with divisibility into groups

B. T. Rumov

V. A. Steklov Mathematical Institute, Academy of Sciences 0f the USSR

Abstract: This paper proves the existence of resolvable block designs with divisibility into groups $GD(v;k,m;\lambda_1,\lambda_2)$ without repeated blocks and with arbitrary parameters such that $\lambda_1=k$, $(v-1)/(k-1)\le\lambda_2\le v^{k-2}$ (and also $\lambda_1\le k/2$), $(v-1)/(2(k-1))\le\lambda_2\le v^{k-2}$ in case $k$ is even) $k\ge4$ and $p\equiv1\pmod{k-1}$, $k<p$ for each prime divisor $p$ of number $v$. As a corollary, the existence of a resolvable $BIB$-design $(v,k,\lambda)$ without repeated blocks is deduced with $\lambda=k$ (and also with $\lambda=k/2$ in case of even $k$) $k>\sqrt{p}v=pk^\alpha$ , where $\alpha$ is a natural number if $k$ is a prime power $\alpha=1$ if $k$ is a composite number.

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English version:
Mathematical Notes, 1976, 19:4, 376–382

Bibliographic databases:

UDC: 519.1

Citation: B. T. Rumov, “The existence of some resolvable block designs with divisibility into groups”, Mat. Zametki, 19:4 (1976), 623–634; Math. Notes, 19:4 (1976), 376–382

Citation in format AMSBIB
\Bibitem{Rum76} \by B.~T.~Rumov \paper The existence of some resolvable block designs with divisibility into groups \jour Mat. Zametki \yr 1976 \vol 19 \issue 4 \pages 623--634 \mathnet{http://mi.mathnet.ru/mz7782} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=404002} \zmath{https://zbmath.org/?q=an:0338.05010} \transl \jour Math. Notes \yr 1976 \vol 19 \issue 4 \pages 376--382 \crossref{https://doi.org/10.1007/BF01156802}