Occupancy constraints

This chapter introduces a finer level of analysis for counting sequences or collections that are subject to some occupancy constraint, namely a constraint on the number of repetitions of its elements. Several problems are considered. As more unusual application in this framework, we prove the Leibniz rule for the derivatives of a product of functions, and count, in terms of the Catalan numbers, the Dyck sequences, i.e., the binary sequences of even length with equal number of 0’s and 1’s where, at each position, the number of 1’s does not exceed the number of 0’s.