GENERALIZED LATIN SQUARE

  • Iranmanesh A. (Department of Mathematics, Tarbiat Modarres University) ;
  • Ashrafi A.R. (Department of Mathematics, Faculty of Science, University of Kashan)
  • Published : 2006.09.01

Abstract

Let X be a n-set and let A = [aij] be a $n {\times} n$ matrix for which $aij {\subseteq} X$, for $1 {\le} i,\;j {\le} n$. A is called a generalized Latin square on X, if the following conditions is satisfied: $U^n_{i=1}\;aij = X = U^n_{j=1}\;aij$. In this paper, we prove that every generalized Latin square has an orthogonal mate and introduce a Hv-structure on a set of generalized Latin squares. Finally, we prove that every generalized Latin square of order n, has a transversal set.

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