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

  title={A bijection for triangulations of a polygon with interior points and multiple edges},
  author={Dominique Poulalhon and Gilles Schaeffer},
  journal={Theor. Comput. Sci.},
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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