Transportation matrices are $m\times n$ nonnegative matrices with given row sum vector $R$ and column sum vector $S$. All such matrices form the convex polytope $\mathcal{U}(R,S)$ which is called a transportation polytope and its extreme points have been classified. In this article, we consider a new class of convex polytopes $\Delta(\bar{R},\bar{S},\sigma)$ consisting of certain transportation polytopes satisfying that the sum of all elements is $\sigma$, and the row and column sum vectors are dominated componentwise by the given positive vectors $\bar{R}$ and $\bar{S}$, respectively. We characterize the extreme points of $\Delta(\bar{R},\bar{S},\sigma)$. Moreover, we give the minimal term rank and maximal permanent of $\Delta(\bar{R},\bar{S},\sigma)$.

In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix is also proved. In addition, a conjecture about the permanent and permanental minors of square row substochastic matrices with fixed row and column sums is formulated.

In this paper, some inequalities for permanents and permanental minors of row substochastic matrices are proved. The convexity of the permanent function on the interval between the identity matrix and an arbitrary row substochastic matrix is also proved. In addition, a conjecture about the permanent and permanental minors of square row substochastic matrices with fixed row and column sums is formulated.