A bijective census of nonseparable planar maps
Journal of Combinatorial Theory Series A
Left ternary trees and non-separable rooted planar maps
Theoretical Computer Science
Regular Article: Enumeration of Planar Constellations
Advances in Applied Mathematics
Combinatorial Enumeration
Optimizing markov models with applications to triangular connectivity coding
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Bijective counting of Kreweras walks and loopless triangulations
Journal of Combinatorial Theory Series A
Uniform random sampling of planar graphs in linear time
Random Structures & Algorithms
Optimal coding and sampling of triangulations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Algebraic generating functions in enumerative combinatorics and context-free languages
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Unified bijections for maps with prescribed degrees and girth
Journal of Combinatorial Theory Series A
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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 In the much easier case of loopless triangulations of the sphere (k = 3), we recover and prove correct an unpublished construction of the second author.