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ON THE (n, k)-TH CATALAN NUMBERS
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 Title & Authors
ON THE (n, k)-TH CATALAN NUMBERS
Kim, Dong-Seok;
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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.
 Keywords
Catalan numbers;(n,k)-th Catalan numbers;partitions;combinatorial webs;invariant vectors;
 Language
English
 Cited by
1.
Ballot matrix as Catalan matrix power and related identities, Discrete Applied Mathematics, 2012, 160, 3, 344  crossref(new windwow)
2.
Inverting linear combinations of identity and generalized Catalan matrices, Linear Algebra and its Applications, 2010, 433, 7, 1472  crossref(new windwow)
 References
1.
N. Cameron, Randon walks, trees and extensions of Riordan group techniques, Annual joint AMS meeting, Baltimore, MD, 2003

2.
E. Catalan, Note extraite dune lettre adressee, J. Reine Angew. Math. 27 (1844), 192.

3.
W. Chu, A new combinatorial interpretation for generalized Catalan number, Disc. Math. 65 (1987), 91-94 crossref(new window)

4.
J. Conway and R. Guy, The Book of Numbers, Copernicus, New York, 1996

5.
M. Gardner, Time Travel and other Mathematical Bewilderments, W. H. Freeman and Company, New York, 1988

6.
H. Gould, Binomial coefficients, the bracket functions, and compositions with relatively prime summands, The Fibonacci quarterly 4 (1964), no. 2, 241-259

7.
H. Gould, Combinatorial Identities, Morgantown, WV, 1972

8.
F. Harary, et al, On the cell-growth problem for arbitrary polygons, Disc. Math. 11 (1975), 371-389 crossref(new window)

9.
D. Kim, Trihedron coefficient for $U_{q}$(sl(3)), J. Knot Theory Ramifications 15 (2006), no. 4, 453-469 crossref(new window)

10.
D. Kim, Jones-Wenzl idempotents For Rank 2 Simple Lie algebras, Osaka J. Math. 44 (2007), 691-722

11.
D. Kim and J. Lee, The quantum sl(3) invariants of cubic bipartite planar graphs, J. Knot Theory Ramifications 17 (2008), no. 3, 361-375 crossref(new window)

12.
G. Kuperberg, Spiders for rank 2 Lie algebras, Comm. Math. Phys. 180 (1996), no. 1, 109-151 crossref(new window)

13.
R. Stanley, Enumerative combinatorics Vol. 2, Cambridge studies in advanced Mathe-matics, Cambridge, 1999

14.
R. Stanley, Catalan addendum, http://www-math.mit.edu/~rstan/ec/catadd.pdf

15.
T. Van Zandt, PSTricks, PostScript macros for generic TEX, Available at ftp://ftp. princeton.edu/pub/tvz/