AbstractA partition π of the set = {1, 2, . , n} is a collection {B1, . , Bk} ofnonempty disjoint subsets of (called blocks) whose union equals . In thispaper, we find explicit formulas for the generating functions for the number of par-titions of containing exactly k blocks where k is fixed according to the numberof occurrences of a subword pattern τ for several classes of patterns, including allwords of length 3. In addition, we find simple explicit formulas for the total numberof occurrences of the patterns in question within all the partitions of containingk blocks, providing both algebraic and combinatorial proofs...