Critical sets in back circulant Latin rectangles.
E. S. Mahmoodian, Glynda Rees · 1997
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 mn array is a set S of given entries, such that there exists a unique extension of S to a latin rectangle of size mn. If we index the rows and columns of an mn array, m n, by the sets M = 2, . . . , m} and N = 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 /4#.