On the Number of Faces of Certain Transportation Polytopes

Define the transportation polytope Tn, mto be a polytope of non-negative n × m matrices with row sums equal to m and column sums equal ton . We present a new recurrence relation for the numbers fkof the k -dimensional faces for the transportation polytope Tn, n + 1. This gives an efficient algorithm for computing the numbers fk, which solves the problem known to be computationally hard in a general case.