PRUNED HURWITZ NUMBERS
Norman Do, Paul Norbury
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | AMER MATHEMATICAL SOC | Published : 2018
Simple Hurwitz numbers count branched covers of the Riemann sphere and are well-studied in the literature. We define a new enumeration that restricts the count to branched covers satisfying an additional constraint. The resulting pruned Hurwitz numbers determine their simple counterparts, but have the advantage of satisfying simpler recursion relations and obeying simpler formulae. As an application of pruned Hurwitz numbers, we obtain a new proof of the Witten–Kontsevich theorem. Furthermore, we apply the idea of defining useful restricted enumerations to orbifold Hurwitz numbers and Belyi Hurwitz numbers.
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Awarded by Australian Research Council
The authors were partially supported by the Australian Research Council grants DE130100650 (ND) and DP1094328 (PN).