Counting occurrences of some subword patterns

We find generating functions the number of strings (words) containing a specified number of occurrences of certain types of order-isomorphic classes of substrings called subword patterns. In particular, we find generating functions for the number of strings containing a specified number of occurrences of a given 3-letter subword pattern.Comment: 9 page

Counting occurrences of 132 in an even permutation

We study the generating function for the number of even (or odd) permutations on n letters containing exactly r\gs0 occurrences of 132. It is shown that finding this function for a given r amounts to a routine check of all permutations in $S_{2r}$.Comment: 12 pages, 2 figure