On the number of faces of certain transportation polytopes (Q1580679)

Consider a transportation polytope \(T_{n,m}(a,b)\) i.e., the set of non-negative \(n\times m\) matrices with row sums equal to \(m\) and column sums equal to \(n\), where \(a=(a_1, \dots, a_m)\), \(b=(b_1, \dots, b_m)\) are two non-negative integer vectors, such that \(a_1+ \cdots +a_m =b_1+ \cdots +b_n\). In this paper the author presents an efficient algorithm for computing the number of faces of transportation polytopes in a special case when \(n=m+1\), \(a= (m+1, \dots,m+1)\) and \(b=(m,\dots,m)\).