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Cayley’s formula for the number of trees

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Proofs from THE BOOK

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Abstract

One of the most beautiful formulas in enumerative combinatorics concerns the number of labeled trees. Consider the set N = {1, 2,..., n}. How many different trees can we form on this vertex set? Let us denote this number by T n . Enumeration “by hand” yields T 1 = 1, T 2 = 1, T 3 = 3, T 4 = 16, with the trees shown in the following table

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References

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Authors and Affiliations

  1. Institut für Mathematik II (WE2), Freie Universität Berlin, Arnimallee 3, 14195, Berlin, Germany

    Martin Aigner

  2. Institut für Mathematik, MA 6-2, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Günter M. Ziegler

Authors
  1. Martin Aigner
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  2. Günter M. Ziegler
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© 2001 Springer-Verlag Berlin Heidelberg

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Aigner, M., Ziegler, G.M. (2001). Cayley’s formula for the number of trees. In: Proofs from THE BOOK. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04315-8_24

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  • DOI: https://doi.org/10.1007/978-3-662-04315-8_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-04317-2

  • Online ISBN: 978-3-662-04315-8

  • eBook Packages: Springer Book Archive

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