Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2008; 23(3): 349-356

Printed September 1, 2008

Copyright © The Korean Mathematical Society.

On the $(n,k)$-th Catalan numbers

Dongseok Kim

Kyonggi University

Abstract

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In this paper, we generalize the Catalan number to the $(n,k)$-th Catalan numbers and find a combinatorial description that the $(n,k)$-th Catalan numbers is equal to the number of partitions of $n(k-1)+2$ polygon by $(k+1)$-gon where all vertices of all $(k+1)$-gons lie on the vertices of $n(k-1)+2$ polygon.

Keywords: Catalan numbers, $(n,k)$-th Catalan numbers, partitions, combinatorial webs, invariant vectors

MSC numbers: Primary 05A19; Secondary 17B10, 05C05

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