  We consider the set partition statistics ls and rb introduced by Wachs and
White and investigate their distribution over set partitions avoiding certain
patterns. In particular, we consider those set partitions avoiding the pattern
13/2, $\Pi_n(13/2)$, and those avoiding both 13/2 and 123, $\Pi_n(13/2,123)$.
We show that the distribution over $\Pi_n(13/2)$ enumerates certain integer
partitions, and the distribution over $\Pi_n(13/2,123)$ gives q-Fibonacci
numbers. These q-Fibonacci numbers are closely related to q-Fibonacci numbers
studied by Carlitz and by Cigler. We provide combinatorial proofs that these
q-Fibonacci numbers satisfy q-analogues of many Fibonacci identities. Finally,
we indicate how p,q-Fibonacci numbers arising from the bistatistic (ls, rb)
give rise to p,q-analogues of identities.
