Permutations and words counted by consecutive patterns

Generating functions which count occurrences of consecutive sequences in a permutation or a word which matches a given pattern are studied by exploiting the combinatorics associated with symmetric functions. Our theorems take the generating function for the number of permutations which do not contain a certain pattern and give generating functions refining permutations by the both the total number of pattern matches and the number of nonoverlapping pattern matches. Our methods allow us to give new proofs of several previously recorded results on this topic as well as to prove new extensions and new q-analogues of such results.