W-operators and generating functions of hurwitz numbers

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

Sun, Hao

关键词: W-operator, Hurwitz number, Cut-and-join operator;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/101336/SUN-DISSERTATION-2018.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.