Pairwise Balanced Design of Order 6n+4 and 2-Fold System of Order 3n+2

Pairwise Balanced Design of Order 6n+4 and 2-Fold System of Order 3n+2

In the Steiner triple system, Bose (1939) constructed the 2−(v,3,1) design for v=6n+3 and later on Skolem (1958) 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, w...

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Veröffentlicht in:ISRN Discrete Mathematics. 2012-01, Vol.2012 (2012), p.1-7
Hauptverfasser: Basu, Manjusri, Ghosh, Debabrata Kumar, Bagchi, Satya
Format: Artikel
Sprache:eng
Schlagworte:
Balancing
Construction
Design engineering
Mathematical analysis
Studies
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Zusammenfassung:In the Steiner triple system, Bose (1939) constructed the 2−(v,3,1) design for v=6n+3 and later on Skolem (1958) 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∈N.
ISSN:2090-777X
2090-7788
DOI:10.5402/2012/251457