A combinatorial proof of Postnikov's identity and a generalized enumeration of labeled trees

Preprint English OPEN
Seo, Seunghyun;
(2004)
  • Subject: Mathematics - Combinatorics | 05C05, 05C30 (Secondary) | 05A15 (Primary)

In this paper, we give a simple combinatorial explanation of a formula of A. Postnikov relating bicolored rooted trees to bicolored binary trees. We also present generalized formulas for the number of labeled k-ary trees, rooted labeled trees, and labeled plane trees.
  • References (5)

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    [2] J. Pitman and R. P. Stanley, A polytope related to empirical distributions, plane trees, parking functions, and the associahedron, Discrete Comput. Geom. 27 (2002), no. 4, 603-634.

    [3] A. Postnikov, Permutohedra, associahedra, and beyond, Retrospective in Combinatorics: Honoring Richard Stanley's 60th Birthday, Massachusetts Institute of Technology, Cambridge, Massachusetts, 2004, slide available at: http://www-math.mit.edu/~apost/talks/perm-slides.pdf

    [4] R. P. Stanley, Enumerative Combinatorics, Vol. 2, Cambridge University Press, Cambridge, 1999.

    [5] D. Stanton and D. White, Constructive Combinatorics, Springer-Verlag, New York, 1986.

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