The rank distribution of the maximin in a random matrix

Let S be a set of tm distinct real numbers and R a random t × m matrix of these tm numbers with rows {r_i} and columns (c_i}. Define b = Max Min x. l≤i≤t x?r_i. Let c be the event Max Min x = Min Max x. l≤i≤t x?r_i l≤i≤m x?c_i. This paper derives the probability distribution of the rank of b in S, as well as the same distribution conditional on c.