A bijection for triangulations of a polygon with interior points and multiple edges

@article{Poulalhon2003ABF,
  title={A bijection for triangulations of a polygon with interior points and multiple edges},
  author={Dominique Poulalhon and Gilles Schaeffer},
  journal={Theor. Comput. Sci.},
  year={2003},
  volume={307},
  pages={385-401}
}
Loopless triangulations of a polygon with k vertices in k + 2n triangles (with interior points and possibly multiple edges) were enumerated by Mullin in 1965, using generating functions and calculations with the quadratic method. In this article we propose a simple bijective interpretation of Mullin’s formula. The argument rests on the method of conjugacy classes of trees, a variation of the cycle lemma designed for planar maps. In the much easier case of loopless triangulations of the sphere… CONTINUE READING

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References

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Showing 1-10 of 15 references

Census of planar maps: from the one-matrix model solution to a combinatorial proof

  • J. Bouttier, P. D. Francesco, E. Guitter
  • SPhT/02-093, arXiv:cond-mat/0207682
  • 2002

ProblV emes T enumT eratifs sur les factorisations et les cartes planaires

  • D. Poulalhon
  • Ph.D. Thesis, T Ecole Polytechnique, France
  • 2002
1 Excerpt

Schae-er, The degree distribution in bipartite planar maps: applications to the Ising model, 32pp

  • G. M. Bousquet-MT elou
  • 2002

Schae-er, Enumeration of planar constellations

  • G. M. Bousquet-MT elou
  • Adv. Appl. Math
  • 2000
2 Excerpts

Conjugaison d’arbres et cartes combinatoires alT eatoires

  • G. Schae-er
  • Ph.D. Thesis, UniversitT e Bordeaux I, France
  • 1998
2 Excerpts

Combinatorial Enumeration

  • I. P. Goulden, D. M. Jackson
  • Wiley, New York
  • 1983

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