Tropical determinant of integer doubly-stochastic matrices (Q665944)

The authors find a sharp upper bound of the set \(D(m,n)\) of all the integer points in the \(m\)-dilate of the Birkhoff polytope of bi-stochastic \(n\times n\)-matrices. They introduce a version of the tropical determinant where the maximum over all the transversals in a matrix is replaced with the minimum and then find a sharp lower bound on thus defined tropical determinant over \(D(m,n)\).