Geodesic
Distribution of crossings, nestings and alignments of two edges in matchings and partitions
The electronic journal of combinatorics, Tome 13 (2006)

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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 in 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.
DOI : 10.37236/1059
Classification : 05A18, 05A15, 05A30 
Anisse Kasraoui; Jiang Zeng. Distribution of crossings, nestings and alignments of two edges in matchings and partitions. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1059
@article{10_37236_1059,
     author = {Anisse Kasraoui and Jiang Zeng},
     title = {Distribution of crossings, nestings and alignments of two edges in matchings and partitions},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1059},
     zbl = {1096.05006},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1059/}
}
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