Critical Sets of 2-Balanced Latin Rectangles |
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Authors: | Nicholas Cavenagh Vaipuna Raass |
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Institution: | 1.Department of Mathematics,The University of Waikato,Hamilton,New Zealand |
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Abstract: | An (m, n, 2)-balanced Latin rectangle is an \({m \times n}\) array on symbols 0 and 1 such that each symbol occurs n times in each row and m times in each column, with each cell containing either two 0’s, two 1’s or both 0 and 1. We completely determine the structure of all critical sets of the full (m, n, 2)-balanced Latin rectangle (which contains 0 and 1 in each cell). If m, \({n \geq 2}\), the minimum size for such a structure is shown to be \({(m-1)(n-1)+1}\). Such critical sets in turn determine defining sets for (0, 1)-matrices. |
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