学位论文详细信息
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.
【 预 览 】
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W-operators and generating functions of hurwitz numbers | 720KB | download |