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- W1969632028 abstract "A partition of the set [n]={1, 2, …, n} is a collection {B1, …, Bk} of nonempty disjoint subsets of [n] (called blocks) whose union equals [n]. A partition of [n] is said to be smooth if i ∈ Bs implies that i + 1 ∈ Bs−1 ∪ Bs ∪ Bs+1 for all i ∈ [n − 1] (B0 = Bk + 1 = ∅). This paper presents the generating function for the number of k-block, smooth partitions of [n], written in terms of Chebyshev polynomials of the second kind. There follows a formula for the number of k-block, smooth partitions of [n] written in terms of trigonometric sums. Also, by first establishing a bijection between the set of smooth partitions of [n] and a class of symmetric Dyck paths of semilength 2n − 1, we prove that the counting sequence for smooth partitions of [n] is Sloane's A005773." @default.
- W1969632028 created "2016-06-24" @default.
- W1969632028 creator A5024416044 @default.
- W1969632028 date "2009-09-22" @default.
- W1969632028 modified "2023-09-23" @default.
- W1969632028 title "Smooth partitions and Chebyshev polynomials" @default.
- W1969632028 cites W1791927140 @default.
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- W1969632028 doi "https://doi.org/10.1112/blms/bdp071" @default.
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