Generating functions for weighted Hurwitz numbers
Generating functions for weighted Hurwitz numbers
Double Hurwitz numbers enumerating weighted n-sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of Sn generated by transpositions are determined by an associated weight generating function. A uniquely determined 1-parameter family of 2D Toda τ-functions of hypergeometric type is shown to consist of …