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Title:W-operators and generating functions of hurwitz numbers
Author(s):Sun, Hao
Director of Research:Bergvelt, Maarten
Doctoral Committee Chair(s):Kedem, Rinat
Doctoral Committee Member(s):Di Francesco, Philippe; Nevins, Thomas
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):W-operator, Hurwitz number, Cut-and-join operator
Abstract: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.
Issue Date:2018-04-18
Type:Thesis
URI:http://hdl.handle.net/2142/101336
Rights Information:Copyright 2018 Hao Sun
Date Available in IDEALS:2018-09-04
Date Deposited:2018-05


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