On the $(n,k)$-th Catalan numbers
Commun. Korean Math. Soc. 2008 Vol. 23, No. 3, 349-356
Printed September 1, 2008
Dongseok Kim
Kyonggi University
Abstract : 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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