Abstract. Literature shows that there are several ways of generating Latin squares, but there is not enough implementati
IJRIT International Journal of Research in Information Technology, Volume 1, Issue 4, April 2013, Pg. 38-50
International Journal of Research in Information Technology (IJRIT)
www.ijrit.com
ISSN 2001-5569
An Algorithm to Construct Super-Symmetric Latin Squares of Order 2n M.A.P.Chamikara1, S.R.Kodituwakku2, A.A.C.A.Jayathilake3, A.A.I.Perera4 1
Postgraduate Institute of Science, University of Peradeniya, Peradeniya, Sri Lanka. 2
Department of Statistics and Computer Science, Faulty of Science, University of Peradeniya, Sri Lanka
3
Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka
4
Department of Mathematics, University of Peradeniya, Peradeniya, Sri Lanka
[email protected],
[email protected] 2,
[email protected],
[email protected] 4
Abstract Literature shows that there are several ways of generating Latin squares, but there is not enough implementation about Super-symmetric Latin squares. This paper proposes a mathematical algorithm to construct Super-symmetric Latin squares of order 2 by substituting blocks of order 2n which has the basic properties of a recursive algorithm. The proposed algorithm was tested for a large number of orders and the results proved that the algorithm could be generalized for any input order n where n is a positive integer. Keywords: Combinatorics, Design theory, Graph theory, Latin Square, Super-symmetry
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