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Paper   IPM / M / 169
School of Mathematics
Title:   Critical sets in back circulant latin rectangles
Author(s):
 1 E. S. Mahmoodian 2 G.H.J. Van Rees
Status:   Published
Journal: Australas. J. Combin.
Vol.:  16
Year:  1997
Pages:   45-50
Supported by:  IPM
Abstract:
A latin rectangle is an m×n array, mn, 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, mn, 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(nm)+⎣(m−1)2/4⎦.

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