Sorting with two ordered stacks in series
Theoretical Computer Science
A generalization of the language of Łukasiewicz coding rooted planar hypermaps
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
A bijection for triangulations of a polygon with interior points and multiple edges
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Transitive cycle factorizations and prime parking functions
Journal of Combinatorial Theory Series A
Counting unrooted loopless planar maps
European Journal of Combinatorics
Polynomial equations with one catalytic variable, algebraic series and map enumeration
Journal of Combinatorial Theory Series B
On the number of factorizations of a full cycle
Journal of Combinatorial Theory Series A
A biased survey of map enumeration results
MATH'06 Proceedings of the 10th WSEAS International Conference on APPLIED MATHEMATICS
Asymptotic enumeration of constellations and related families of maps on orientable surfaces
Combinatorics, Probability and Computing
Algebraic generating functions in enumerative combinatorics and context-free languages
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
A simple model of trees for unicellular maps
Journal of Combinatorial Theory Series A
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The enumeration of transitive ordered factorizations of a given permutation is a combinatorial problem related to singularity theory. Let n=1, and let @s"0 be a permutation of S"n having d"i cycles of length i, for i=1. Let m=2. We prove that the number of m-tuples (@s"1,...,@s"m) of permutation of S"n such that*@s@s...@s=@s, *the group generated by @s,...,@s acts transitively on {1,2,...,}, *@?(@s)=(-1)+2, where (@s) denotes the number of cycles of @s A one-to-one correspondence relates these m-tuples to some rooted planar maps, which we call constellations and enumerate via a bijection with some bicolored trees. For m=2, we recover a formula of Tutte for the number of Eulerian maps. The proof relies on the idea that maps are conjugacy classes of trees and extends the method previously applied to Eulerian maps by the second author. Our result might remind the reader of an old theorem of Hurwitz, giving the number of m-tuples of transpositions satisfying the above conditions. Indeed, we show that our result implies Hurwitz' theorem. We also briefly discuss its implications for the enumeration of nonequivalent coverings of the sphere.