CONSTRUCTION OF STEINER TRIPLE SYSTEM STS(2n+1) FROM A CLASS OF PAIRWISE BALANCED DESIGNS.

Autor: Popoola, Osuolale Peter, Oyejola, Benjamin A., Ayanrinde, Ayanniyi A., Odusina, Matthew T.
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Zdroj: Annals. Computer Science Series; 2019, Vol. 17 Issue 1, p122-126, 5p
Abstrakt: Pairwise Balanced Design (PBD) is a pair (X, Ɓ) where X is a set of treatments and Ɓ is a collection of subsets of X called blocks, such that each pair of treatments is contained in precisely one block. PBD plays important role in design theories, it is used to construct other important designs such as Steiner Triple System (STS). A Steiner triple system is an ordered pair (X, Ɓ), where X is a finite set of points (Treatments) and B is a set of all 3-element subsets of X called triples, such that each pair of distinct elements of X occurs together in exactly one triple of B. The research work aims at applying a class of PBD(n, K, 1) when K ={3, 4} and λ = 1 to construct STS(2n +1). Theorem was proposed and proved and a certain inequality was derived as condition which must be satisfied for the construction to hold. Thus, for all n ≡ 1, 3(mod 3) of any PBD(n, {3, 4}) there exists an STS(2n +1) provided n ≥ l(s -1) + 1, where l is the size of the largest block of the PBD and s is the size of the smallest block of the PBD. Hence, STS(21) was constructed from a PBD(10, {3, 4}, 1). [ABSTRACT FROM AUTHOR]
Databáze: Supplemental Index