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arXiv · 1712.05639

Signed counts of real simple rational functions

Boulos El Hilany·Johannes Rau
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Abstract

We study the problem of counting real simple rational functions $φ$ with prescribed ramification data (i.e. a particular class of oriented real Hurwitz numbers of genus $0$). We introduce a signed count of such functions that is invariant under change of the branch locus, thus providing a lower bound for the actual count (which does depend on such change). We prove (non-)vanishing theorems for these signed counts and study their asymptotic growth when adding further simple branch points. The approach is based on the works of Itenberg and Zvonkine (arXiv:1609.05219) which treat the polynomial case.

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Boulos El Hilany, Johannes Rau. 2019-10-11. Signed counts of real simple rational functions. https://doi.org/10.1007/s10801-019-00906-6

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