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

✍ Scribed by Dominique Poulalhon; Gilles Schaeffer

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 368 KB
Volume: 307
Category: Article
ISSN: 0304-3975
DOI: 10.1016/s0304-3975(03)00226-3

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✦ Synopsis

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 In the much easier case of loopless triangulations of the sphere (k = 3), we recover and prove correct an unpublished construction of the second author.

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