  An avoidance pattern where the letters within an occurrence of which are
required to be adjacent is referred to as a subword. In this paper, we
enumerate members of the set NC_n of non-crossing partitions of length n
according to the number of occurrences of several infinite families of subword
patterns each containing repeated letters. As a consequence of our results, we
obtain explicit generating function formulas counting the members of NC_n for n
>= 0 according to all subword patterns of length three containing a repeated
letter. Further, simple expressions are deduced for the total number of
occurrences over all members of NC_n for the various families of patterns.
Finally, combinatorial proofs can be given explaining three infinite families
of subword equivalences over NC_n, which generalize the following equivalences:
211 = 221, 1211 = 1121 and 112 = 122.
