Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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A REFINED ENUMERATION OF p-ARY LABELED TREES

  • Seo, Seunghyun (Department of Mathematics Education Kangwon National University) ;
  • Shin, Heesung (Department of Mathematics Inha University)
  • Received : 2013.11.29
  • Accepted : 2013.12.26
  • Published : 2013.12.30
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Abstract

Let $\mathcal{T}^{(p)}_n$ be the set of p-ary labeled trees on $\{1,2,{\ldots},n\}$. A maximal decreasing subtree of an p-ary labeled tree is defined by the maximal p-ary subtree from the root with all edges being decreasing. In this paper, we study a new refinement $\mathcal{T}^{(p)}_{n,k}$ of $\mathcal{T}^{(p)}_n$, which is the set of p-ary labeled trees whose maximal decreasing subtree has k vertices.

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References

  1. Francois Bergeron, Philippe Flajolet, and Bruno Salvy, Varieties of increasing trees, In CAAP '92 (Rennes, 1992), volume 581 of Lecture Notes in Comput. Sci., pages 24-48. Springer, Berlin, 1992.
  2. Ronald L. Graham, Donald E. Knuth, and Oren Patashnik, Concrete mathematics, Addison-Wesley Publishing Company Advanced Book Program, Reading, MA, 1989.
  3. Seunghyun Seo and Heesung Shin, A generalized enumeration of labeled trees and reverse Prufer algorithm, J. Combin. Theory Ser. A. 114 (7) (2007), 1357-1361. https://doi.org/10.1016/j.jcta.2007.01.010
  4. Seunghyun Seo and Heesung Shin, On the enumeration of rooted trees with fixed size of maximal decreasing trees, Discrete Math. 312 (2) (2012), 419-426. https://doi.org/10.1016/j.disc.2011.10.001
  5. Seunghyun Seo and Heesung Shin, A refinement for ordered labeled trees, Korean J. Math. 20 (2) (2012), 255-261. https://doi.org/10.11568/kjm.2012.20.2.255
  6. Richard P. Stanley, Enumerative combinatorics. Vol. 2, volume 62 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1999. With a foreword by Gian-Carlo Rota and appendix 1 by Sergey Fomin.