Multispecies quantum Hurwitz numbers

Abstract

The construction of hypergeometric 2D Toda $\tau$-functions as generating functions for quantum Hurwitz numbers is extended here to multispecies families. Both the enumerative geometrical significance of these multispecies quantum 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.

11 pages.This is the revised version posted March 30, 2015

References in corpus (2)

• Hypergeometric τ-functions, Hurwitz numbers and enumeration of paths
• Hurwitz numbers and BKP hierarchy

Cited by in corpus (5)

• Toda hierarchies and their applications
• Multispecies Weighted Hurwitz Numbers
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• Matrix integrals and Hurwitz numbers
• $q$-Difference Kac-Schwarz Operators in Topological String Theory