Enumeration of planar constellations

  title={Enumeration of planar constellations},
  author={Mireille Bousquet-M{\'e}lou and Gilles Schaeffer},
The enumeration of transitive ordered factorizations of a given permutation is a combinatorial problem related to singularity theory. Let n > 1, and let 0 be a permutation of Sn having di cycles of length i, for i > 1. Let m > 2. We prove that the number of m-tuples (1 ; : : : ; m) of permutations of Sn such that: 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… CONTINUE READING
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