Partitions with \(k\) crossings
type: Item
instance of: scholarly article
title: Partitions with \(k\) crossings
zbMATH Open document ID: 0933.05003
DOI: 10.1023/A:1006901625470
author: Miklós Bóna
published in: The Ramanujan Journal
publication date: 2000-04-04T00:00:00Z
review text: The author proves that the ordinary generating function \(S_k(x)\) for the number \(S_k(n)\) of partitions of the set \(\{1,2,\dots,n\}\) with \(k\) crossings [see, e.g., \textit{R. Simion}, J. Comb. Theory, Ser. A 66, No. 2, 270-301 (1994; Zbl 0803.05003)] is a rational function of \(x\) and the ordinary generating function of the Catalan numbers. In particular, \(S_1(n)= \left(\begin{smallmatrix} 2n-5\\ n-4\end{smallmatrix}\right)\). This sequence first found by A. Cayley in 1890 is used in various counting problems.
reviewed by: Indulis Strazdins
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05A05
Mathematics Subject Classification ID: 05A18
zbMATH DE Number: 1347444
zbMATH Keywords: set partition
zbMATH Keywords: generating function
zbMATH Keywords: Catalan numbers
zbMATH Keywords: counting problems
MaRDI profile type: Publication
full work available at URL: a:1006901625470
OpenAlex ID: W1571912376
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description: scientific article; zbMATH DE number 1347444