An MCA ∼ defines a partition of the set of all word indices c ik {c i k }, which is of size n |c| = i n i .
the number of distinct MCAs of G is the number of partitions of a set of size n. This number is called the n th Bell number (Rota, 1964)  Asymptotically, B n grows faster than an exponential but slower than a factorial.