• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

О разложениях циклической перестановки в произведение данного числа перестановок

The investigation of decompositions of a permutation into a product of permutations

satisfying certain conditions plays a key role in the study of meromorphic functions or, equivalently,

branched coverings of the 2-sphere; it goes back to A. Hurwitz' work in the late nineteenth century.

In 2000 M. Bousquet-Melou and G. Schaeffer obtained an elegant formula for the number of decompositions

of a permutation into a product of a given number of permutations corresponding to

coverings of genus 0. Their formula has not been generalized to coverings of the sphere by surfaces of

higher genera so far. This paper contains a new proof of the Bousquet-Melou-Schaeffer formula for

the case of decompositions of a cyclic permutation, which, hopefully, can be generalized to positive

genera.