Pairwise balanced design of order \(6n+4\) and 2-fold system of order \(3n+2\) (Q1935973)
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scientific article; zbMATH DE number 6137694
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pairwise balanced design of order \(6n+4\) and 2-fold system of order \(3n+2\) |
scientific article; zbMATH DE number 6137694 |
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Pairwise balanced design of order \(6n+4\) and 2-fold system of order \(3n+2\) (English)
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21 February 2013
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Summary: In the Steiner triple system, \textit{R.C. Bose} [Ann. of Eugen. 9, 353--399 (1939; Zbl 0023.00102)] constructed the \(2\)-\((v, 3, 1)\) design for \(v = 6n+3\) and later on \textit{T. Skolem} [Math. Scand. 6, 273--280 (1958; Zbl 0105.25002)] constructed the same for \(v = 6n+1\). In the literature we found a pairwise balanced design (PBD) for \(v = 6n+5\). We also found the 2-fold triple system of the orders \(3n\) and \(3n+1\). In this paper, we construct a PBD for \(v = 6n+4\) and a 2-fold system of the order \(3n + 2\). The second construction completes the 2-fold system for all \(n \in N\).
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Steiner triple system
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pairwise balanced design
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PBD
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2-fold system
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