Generalized latin square |
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| Authors: | A Iranmanesh A R Ashrafi |
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| Institution: | 1. Department of Mathematics, Tarbiat Modarres University, P.O.Box: 14115-137, Tehran, Iran
2. Department of Mathematics Faculty of Science, University of Kashan, Kashan, Iran
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| Abstract: | LetX be a n-set and letA = aij] be an xn matrix for whichaij ?X, for 1 ≤i, j ≤n. A is called a generalized Latin square onX, if the following conditions is satisfied: $ \cup _{i = 1}^n a_{ij} = X = \cup _{j = 1}^n a_{ij} $ . 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 ordern, has a transversal set. |
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