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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A simple and direct derivation
for the number of noncrossing partitions


Authors: S. C. Liaw, H. G. Yeh, F. K. Hwang and G. J. Chang
Journal: Proc. Amer. Math. Soc. 126 (1998), 1579-1581
MSC (1991): Primary 05A18
MathSciNet review: 1468196
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Abstract: Kreweras considered the problem of counting noncrossing partitions of the set $\{1,2,\cdots,n\}$, whose elements are arranged into a cycle in its natural order, into $p$ parts of given sizes $n_1,n_2,\cdots,n_p$ (but not specifying which part gets which size). He gave a beautiful and surprising result whose proof resorts to a recurrence relation. In this paper we give a direct, entirely bijective, proof starting from the same initial idea as Kreweras' proof.


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Additional Information

G. J. Chang
Email: gjchang@math.nctu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04546-8
PII: S 0002-9939(98)04546-8
Received by editor(s): November 6, 1996
Additional Notes: Liaw, Yeh, and Chang were supported in part by the National Science Council under grant NSC86-2115-M009-002.
Communicated by: Jeffry N. Kahn
Article copyright: © Copyright 1998 American Mathematical Society