Monotone Hurwitz numbers in genus zero

@inproceedings{Goulden2012MonotoneHN,
  title={Monotone Hurwitz numbers in genus zero},
  author={Ian P. Goulden and Mathieu Guay-Paquet and Jonathan Novak},
  year={2012}
}
Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of the branched covers counted by the Hurwitz numbers, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two… CONTINUE READING

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