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Mat. Zametki, 1974, Volume 15, Issue 4, Pages 551–560 (Mi mz7378)  

This article is cited in 2 scientific papers (total in 2 papers)

A method of constructing generalized difference sets

B. T. Rumov

Steklov Mathematical Institute, Academy of Sciences of the USSR

Abstract: On the elements of the ring of residues modulo $v(2\nmid v,3\nmid v)$ we construct cyclic PBIB-designs with $\tau(v)-1$ classes of connectedness, where $\tau(v)$ is the number of divisors of $v$. We prove the existence of cyclic BIB-designs with parameters $b$, $v$, $r$, $k$ and $\lambda$ such that: 1) $\lambda=k$ (and also $\lambda=k/2$ if $k$ is even), $k\ge4$, and $k-1\mid p-1$ for each prime divisor $p$ of the number $v$; 2) $\lambda=(k-l)/2$, $k$ odd, $k\ge3$, $k\mid p-1$ for each prime divisor $p$ of the number $v$.

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English version:
Mathematical Notes, 1974, 15:4, 324–329

Bibliographic databases:

UDC: 511
Received: 12.04.1973

Citation: B. T. Rumov, “A method of constructing generalized difference sets”, Mat. Zametki, 15:4 (1974), 551–560; Math. Notes, 15:4 (1974), 324–329

Citation in format AMSBIB
\Bibitem{Rum74}
\by B.~T.~Rumov
\paper A~method of constructing generalized difference sets
\jour Mat. Zametki
\yr 1974
\vol 15
\issue 4
\pages 551--560
\mathnet{http://mi.mathnet.ru/mz7378}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=349427}
\zmath{https://zbmath.org/?q=an:0309.05015}
\transl
\jour Math. Notes
\yr 1974
\vol 15
\issue 4
\pages 324--329
\crossref{https://doi.org/10.1007/BF01095122}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. B. T. Rumov, “A recursive construction of difference families in noncyclic groups”, Math. USSR-Sb., 27:2 (1975), 251–261  mathnet  crossref  mathscinet  zmath
    2. B. T. Rumov, “Existence of resolvable block designs”, Math. USSR-Sb., 28:3 (1976), 325–337  mathnet  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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