  The problem of linear and circular permutations of n identical objects in m
boxes, where a limit l is imposed on the number of objects in a box, is
considered. In the linear case, where the boxes are arranged as a row, two
methods of solution are described. The first uses the partition diagram that is
modified with prescribed number of zeros, and the second applies a direct
combinatorial approach. Subject to constraints set on the relation between n
and l, results of the combinatorial approach are used to solve the problem
where there are more than one type of objects. These solutions are then
extended for the case of boxes comprising subgroups that are characterized by
different values of l. In the circular case, where the boxes are arranged in
the form of a circle, no direct combinatorial solution in close form is
available. Consequently, in the latter case, the solution relies on the use of
the modified partition diagram. This solution, which involves the application
of multinomial permutations on a circle, is also extended to the case of two
kinds of objects.
