“School of Mathematics”
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| Paper IPM / M / 169 |
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| Abstract: | |||||
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A latin rectangle is an m×n array, m ≤ n, from
the numbers 1,2,…, n such that each of these numbers occur
in each row and in each column at most once. A critical set
in an m×n array is a set S of given entries, such that
there exists a unique extension of S to a latin rectangle of
size m×n. If we index the rows and columns of an m×n array, m ≤ n, by the sets M={1,2,…, m} and
N={1,2,…, n}, respectively, then the array with integer
i+j−1 (mod n) in the position (i,j) is said to be a
back circulant latin rectangle. We show that the size of smallest
critical set in a back circulant latin rectangle of size m×n, with 4m ≤ 3n is equal to m(n−m)+⎣(m−1)2/4⎦.
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