# Labeled Fuss-Catalan Polygon Divisions

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The Catalan numbers have many interpretations in combinatorics, two of them being the number of ways to insert parentheses into a sequence of numbers so that they are grouped into pairs—for example, ((12)3) and (1(23))—and the number of ways to divide a polygon into triangles.

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Contributed by: Robert Dickau (February 2018)

Open content licensed under CC BY-NC-SA

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References

[1] R. P. Stanley, *Enumerative Combinatorics*, Vol. 2, New York: Cambridge University Press, 1999 pp. 212, 234 (Exercise 6.33(c)).

[2] R. L. Graham, D. E. Knuth and O. Patashnik, *Concrete Mathematics: A Foundation for Computer Science*, 2nd ed., Reading, MA: Addison-Wesley, 1994 p. 361.

[3] M. Gardner, *Time Travel and Other Mathematical Bewilderments*, New York: W. H. Freeman, 1988 Chapter 20.

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