{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101336"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101336","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"W-operators and generating functions of hurwitz numbers","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Sun, Hao"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Bergvelt, Maarten","Kedem, Rinat","Di Francesco, Philippe","Nevins, Thomas"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-04T20:47:19Z","date_published":"2018-09-04T20:47:19Z","updated_at":"2026-07-22T22:24:38Z","subjects":["W-operator, Hurwitz number, Cut-and-join operator"],"languages":["en"],"rights":["Copyright 2018 Hao Sun"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101336","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Bergvelt, Maarten","Kedem, Rinat","Di Francesco, Philippe","Nevins, Thomas"]},{"key":"dc:creator","label":"Author","values":["Sun, Hao"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-04T20:47:19Z","2020-09-05T09:15:09Z","2018-04-18","2018-05"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["W-operator, Hurwitz number, Cut-and-join operator"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Hao Sun"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101336"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2020-05-01","The student, Hao Sun, accepted the attached license on 2018-04-17 at 14:47.","The student, Hao Sun, submitted this Dissertation for approval on 2018-04-17 at 14:59.","This Dissertation was approved for publication on 2018-04-18 at 09:36.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12313 on 2018-08-31 at 17:29:30","Made available in DSpace on 2018-09-04T20:47:19Z (GMT). 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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.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2020-05-01","The student, Hao Sun, accepted the attached license on 2018-04-17 at 14:47.","The student, Hao Sun, submitted this Dissertation for approval on 2018-04-17 at 14:59.","This Dissertation was approved for publication on 2018-04-18 at 09:36.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12313 on 2018-08-31 at 17:29:30","Made available in DSpace on 2018-09-04T20:47:19Z (GMT). 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