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ON THE (n, k)-TH CATALAN NUMBERS

김동석
대한수학회 (The Korean Mathematical Society)|2008.07|대한수학회논문집 (Communications of the KMS)|제23권 제3호|pp. 349-356

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참고문헌

키워드

(npartitionsCatalan numbersk)-th Catalan numberscombi- natorial websinvariant vectors.
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초록

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.

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.

참고문헌 (15)

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  7. H. Gould, "Combinatorial Identities" (1972), Morgantown
  8. F. Harary, "On the cell-growth problem for arbitrary polygons", Disc. Math, 11, pp.371~389 (1975)
  9. D. Kim, "Trihedron coefficient for U q(sl(3))", J. Knot Theory Ramifications, 15(4), pp.453~469 (2006)
  10. D. Kim, "Jones-Wenzl idempotents For Rank 2 Simple Lie algebras", Osaka J. Math, 44, pp.691~722 (2007)
  11. D. Kim, "The quantum sl(3) invariants of cubic bipartite planar graphs", J. Knot Theory Ramifications, 17(3), pp.361~375 (2008)
  12. G. Kuperberg, "Spiders for rank 2 Lie algebras", 109–151, 180(1), pp.109~151 (1996)
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  14. [URL]

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