MathDB

4

Part of 2019 Miklós Schweitzer

Problems(1)

m*n matrices of 1..mn where only 1 is the smallest in its row/column

Source: Miklós Schweitzer 2019, Problem 4

12/27/2019
An n×mn \times m matrix is nice if it contains every integer from 11 to mnmn exactly once and 11 is the only entry which is the smallest both in its row and in its column. Prove that the number of n×mn \times m nice matrices is (nm)!n!m!/(n+m−1)!(nm)!n!m!/(n+m-1)!.
combinatorics