An m by n array consists of mn cells in m rows and n columns, where 2 ≤ m ≤ n. A partial transversal in an m by n array is a set of m cells, one from each row and no two from the same column. A transversal in an m by n array is a partial transversal in which m symbols are distinct. Define as the largest integer such that if each symbol in an m by n array appears at most times, then the array must have a transversal. In this article, we first obtain a better lower bound of by using a probabilistic method and then find for certain positive integers m and n.
- m n arrays