A two-parameter CJT refinement of Jucys-Murphy theory interpolates Schur and zonal actions, yields cut-and-join recursions and tropicalizations of b-Hurwitz numbers, and proves piecewise polynomiality of (1+b) times the double b-Hurwitz count.
Real algebraic curves and twisted Hurwitz numbers
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abstract
We provide a direct correspondence between the $b$-Hurwitz numbers with $b=1$ from \cite{ChapuyDolega}, and twisted Hurwtiz numbers from \cite{TwistedHurwitz}. This provides a description of real coverings of the sphere with ramification on the real line in terms of monodromy.
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A refined twist on Hurwitz numbers
A two-parameter CJT refinement of Jucys-Murphy theory interpolates Schur and zonal actions, yields cut-and-join recursions and tropicalizations of b-Hurwitz numbers, and proves piecewise polynomiality of (1+b) times the double b-Hurwitz count.