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A bijection for loopless triangulations of a polygon with interior points

Dominique Poulalhon 1 Gilles Schaeffer 2
2 ADAGE - Applying discrete algorithms to genomics
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : 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 construction of Mullin's formula. The argument rests on \emph{conjugation of trees}, a variation of the cycle lemma designed for planar maps. In the much easier case of loopless triangulations of the sphere ($k=3$), we recover and prove correct an unpublished construction of the second author.
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Submitted on : Tuesday, September 26, 2006 - 2:52:29 PM
Last modification on : Friday, February 26, 2021 - 3:28:02 PM

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Dominique Poulalhon, Gilles Schaeffer. A bijection for loopless triangulations of a polygon with interior points. International Conference on Formal Power Series and Algebraic Combinatorics - FPSAC'02, Foda, O. and Guttmann, T., Jul 2002, Melbourne, Australie, France. 12 p. ⟨inria-00100860⟩

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