Hodge integrals, Hurwitz numbers, and Symmetric Groups

Abstract

We prove some combinatorial results related to a formula on Hodge integrals conjectured by Mariño and Vafa. These results play important roles in the proof and applications of this formula by the author jointly with Chiu-Chu Melissa Liu and Kefeng Liu. We also compare with some related results on Hurwitz numbers and obtain some closed expressions for the generating series of Hurwitz numbers and the related Hodge integrals.

24 pages

References in corpus (3)

• The Hurwitz Enumeration Problem of Branched Covers and Hodge Integrals
• The Symplectic Sum Formula for Gromov-Witten Invariants
• Virasoro algebra and wreath product convolution

Cited by in corpus (19)

• Complete Set of Cut-and-Join Operators in Hurwitz-Kontsevich Theory
• BGWM as Second Constituent of Complex Matrix Model
• Unitary Integrals and Related Matrix Models
• Local Mirror Symmetry for One-Legged Topological Vertex
• Curve counting and instanton counting
• A Conjecture on Hodge Integrals
• Localizations on Moduli Spaces and Free Field Realizations of Feynman Rules
• Nonlinear PDEs for Fredholm determinants arising from string equations
• Generalized string equations for double Hurwitz numbers
• Quantum Mirror Curves for ${\mathbb{C}}^3$ and the Resolved Confiold
• Formulae of one-partition and two-partition Hodge integrals
• On a Proof of a Conjecture of Marino-Vafa on Hodge Integrals
• Hodge Integrals and Integrable Hierarchies
• Polynomial recursion formula for linear Hodge integrals
• Lectures on the ELSV formula
• Diagonal Tau-Functions of 2D Toda Lattice Hierarchy, Connected $(n,m)$-Point Functions, and Double Hurwitz Numbers
• Localization and Conjectures from String Duality
• Some results of Marino-Vafa formula
• A Formula of Two-Partition Hodge Integrals