Corpus ID: 2643347

Action Graphs and Catalan Numbers

@article{Alvarez2015ActionGA,
  title={Action Graphs and Catalan Numbers},
  author={Gerardo Alvarez and Julia E. Bergner and Rub{\'e}n L{\'o}pez},
  journal={J. Integer Seq.},
  year={2015},
  volume={18},
  pages={15.7.2}
}
We introduce an inductively defined sequence of directed graphs and prove that the number of edges added at step $k$ is equal to the $k$th Catalan number. Furthermore, we establish an isomorphism between the set of edges adjoined at step $k$ and the set of planar rooted trees with $k$ edges. 

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References

SHOWING 1-8 OF 8 REFERENCES
Catalan Numbers with Applications
1. Bionomial Coefficients 2. The Central Binomial Coefficient 3. The Central Binomial Coefficient Revisited 4. Binomial Coeffiecients Revisited 5. Catalan Numbers 6. The Ubiquity of Catalan Numbers IExpand
Reedy categories which encode the notion of category actions
We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we defineExpand
Concerned with sequences A000108 and A014137.) Received March 2 2015; revised version received
  • Published in Journal of Integer Sequences
  • 2015
Mathematics Subject Classification: Primary 05A19, Secondary 05C05. Keywords: Catalan number, directed graph. (Concerned with sequences A000108 and A014137.) Received ; revised version received
  • Published in Journal of Integer Sequences . Return to Journal of Integer Sequences home page
  • 2010
On-Line Encyclopedia of Integer Sequences
Cambridge Studies in Advanced Mathematics
  • Cambridge Studies in Advanced Mathematics
  • 1999
Catalan Addendum, http://www-math.mit.edu/ ~ rstan/ec/catadd
  • 2010 Mathematics Subject Classification: Primary 05A19, Secondary 05C05. Keywords: Catalan number
Return to Journal of Integer Sequences
  • Return to Journal of Integer Sequences