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THE CONSTRUCTION AND MAXIMAL SET OF MUTUALLY ORTHOGONAL LATIN SQUARES | ||
| Journal of University of Anbar for Pure Science | ||
| Article 19, Volume 1, Issue 1, 2007, Pages 76-81 PDF (440.84 K) | ||
| Document Type: Research Paper | ||
| DOI: 10.37652/juaps.2007.15496 | ||
| Author | ||
| MAKARIM A. AL-TURKY* | ||
| COMPUTER COLLEGE - UNIVESITY OF AL-ANBAR | ||
| Abstract | ||
| Given aset of permutation {p1,p2, … . pk} on aset S, we say that the set of permutation is transitive on S if for every ordered pair of elements a,b € S, there exists at least on Pi for which (a) Pi=b. A permutation set for which there is exactly one Pi which maps a to b is called Sharply transitive.For example, if on the set consisting of the three elements {1,2,3} we represent the permutation which maps 1 3 ,2 2 and 3 1by (321). Then the following set of permutation is transitive.(123),(132),(213) and (321) and the last three permutation form sharply transitive set. This construction give a set of mutually orthogonal latin squares. A set S of mutually orthogonal latin squares(MOLS) is maximal if no latin square is orthogonal to each member of S. | ||
| Keywords | ||
| Construction; Maximal Set; Mutually Orthogonal Latin Squares | ||
| References | ||
|
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[5]. Bose, R.C. & Shrikhande, S.S., “On the construction of sets of mutually orthogonal latin squares and Falsity of a conjecture of Euler Transactions of the American Mathematical Society, 95 (1960), PP. 191-209.
[6]. H.B. Mann “on orthogonal latin squares”, Bulletin of the American Mathematical society, 50 (1944), PP.249-257.
[7]. David A. Darke, G.H.J. Van Rees, W.D.Wallis, “Maximal sets of mutually orthogonal latin squeres” Discrete Mathematics, 194 (1999), PP.87-94.
[8]. D. Jungnickel, Maximal sets of mutually orthogonal latin squares, in: S.Cohen, H. Niederraiter Eds). Proc. 3rd Intern. Conf. at Univ. Glasgow, 1995, London Math. Soc. Lecture Note Series, 233, Cambridge Univ. Press, Cambridge, 1996, PP.129-153.
[9]. E.T. Parker, Noextendibility conditions on mutually orthogonal latin squares, Proc. Amer. Math. Soc. 13 (1962), PP. 219-221. | ||
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