Multispecies Weighted Hurwitz Numbers

Abstract

The construction of hypergeometric $2D$ Toda $\tau$-functions as generating functions for weighted Hurwitz numbers is extended to multispecies families. Both the enumerative geometrical significance of multispecies weighted Hurwitz numbers, as weighted enumerations of branched coverings of the Riemann sphere, and their combinatorial significance in terms of weighted paths in the Cayley graph of $S_n$ are derived. The particular case of multispecies quantum weighted Hurwitz numbers is studied in detail.

this is substantially enhanced version of arXiv:1410.8817

References in corpus (5)

• Hypergeometric τ-functions, Hurwitz numbers and enumeration of paths
• Hurwitz numbers, matrix models and enumerative geometry
• Hurwitz numbers and BKP hierarchy
• Multispecies quantum Hurwitz numbers
• Weighted Hurwitz numbers and hypergeometric $\tau$-functions: an overview

Cited by in corpus (6)

• Generating functions for weighted Hurwitz numbers
• Quantum Hurwitz numbers and Macdonald polynomials
• Rationally weighted Hurwitz numbers, Meijer $G$-functions and matrix integrals
• Constellations and $\tau$-functions for rationally weighted Hurwitz numbers
• Generating weighted Hurwitz numbers
• Spectral curves for hypergeometric Hurwitz numbers