Kasraoui, Anisse; Zeng, Jiang Distribution of crossings, nestings and alignments of two edges in matchings and partitions. (English) Zbl 1096.05006 Electron. J. Comb. 13, No. 1, Research paper R33, 12 p. (2006). Summary: We construct an involution on set partitions which keeps track of the numbers of crossings, nestings and alignments of two edges. We derive then the symmetric distribution of the numbers of crossings and nestings in partitions, which generalizes a recent result of Klazar and Noy on perfect matchings. By factorizing our involution through bijections between set partitions and some path diagrams we obtain the continued fraction expansions of the corresponding ordinary generating functions. Cited in 4 ReviewsCited in 25 Documents MSC: 05A18 Partitions of sets 05A15 Exact enumeration problems, generating functions 05A30 \(q\)-calculus and related topics PDF BibTeX XML Cite \textit{A. Kasraoui} and \textit{J. Zeng}, Electron. J. Comb. 13, No. 1, Research paper R33, 12 p. (2006; Zbl 1096.05006) Full Text: EMIS EuDML arXiv