  The permanent of a multidimensional matrix is the sum of products of entries
over all diagonals. By Minc's conjecture, there exists a reachable upper bound
on the permanent of 2-dimensional (0,1)-matrices. In this paper we obtain some
generalizations of Minc's conjecture to the multidimensional case. For this
purpose we prove and compare several bounds on the permanent of
multidimensional (0,1)-matrices. Most estimates can be used for matrices with
nonnegative bounded entries.
