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- W2952862453 abstract "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." @default.
- W2952862453 created "2019-06-27" @default.
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- W2952862453 date "2007-07-18" @default.
- W2952862453 modified "2023-09-27" @default.
- W2952862453 title "Set partition statistics and q-Fibonacci numbers" @default.
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