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ISRN Discrete Mathematics
Volume 2011 (2011), Article ID 534628, 8 pages
http://dx.doi.org/10.5402/2011/534628
Research Article

Some Combinatorial Interpretations and Applications of Fuss-Catalan Numbers

Department of Mathematics, National Taiwan University, Taipei 10617, Taiwan

Received 1 August 2011; Accepted 25 August 2011

Academic Editors: L. Ji and K. Ozawa

Copyright © 2011 Chin-Hung Lin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fuss-Catalan number is a family of generalized Catalan numbers. We begin by two definitions of Fuss-Catalan numbers and some basic properties. And we give some combinatorial interpretations different from original Catalan numbers. Finally we generalize the Jonah's theorem as its applications.