  Let D(m,n) be the set of all the integer points in the m-dilate of the
Birkhoff polytope of doubly-stochastic n by n matrices. In this paper we find
the sharp upper bound on the tropical determinant over the set D(m,n). We
define a version of the tropical determinant where the maximum over all the
transversals in a matrix is replaced with the minimum and then find the sharp
lower bound on thus defined tropical determinant over D(m,n).
