W-operators and generating functions of hurwitz numbers

This thesis is motivated by the W-operators introduced by Mironov et al. We prove that the W-operators are generalizations of the cut-and-join operator studied by Goulden and Jackson. We give a new description of the structure of W-operators, using the combinations of symmetric groups. As an application, we prove new formulas about generating functions of connected Hurwitz numbers and give topological recursion formulas for d-Hurwitz numbers.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Sun, Hao

Contributors dc:contributor

• Bergvelt, Maarten
• Kedem, Rinat
• Di Francesco, Philippe
• Nevins, Thomas

• W-operator, Hurwitz number, Cut-and-join operator

Statement dc:rights

• Copyright 2018 Hao Sun

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101336

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101336