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arXiv · 1501.06799

On the (n,k)-th Catalan numbers

Dongseok Kim
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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.

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Dongseok Kim. 2015-01-27. On the (n,k)-th Catalan numbers. https://arxiv.org/abs/1501.06799

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