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- W101857405 abstract "The generalized Catalan numbers wn are given by the recurrence wn = 2wn−1 + ∑n−2 i=1 wiwn−2−i if n ≥ 2, with w0 = w1 = 1, and count a restricted subset of the Catalan paths having semilength n. In this paper, we provide new combinatorial interpretations of these numbers in terms of nite set partitions. In particular, we identify ve classes of the partitions of size n, all of which have cardinality wn and each avoiding a set of two classical patterns of length four. We use both combinatorial and algebraic arguments to establish our results, applying the kernel method in a couple of the apparently more di cult cases. Mathematics Subject Classi cation(2010). 05A18, 05A15." @default.
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- W101857405 date "2012-01-01" @default.
- W101857405 modified "2023-09-23" @default.
- W101857405 title "Restricted partitions and generalized Catalan numbers" @default.
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