{"id":{"repo_id":"ku","oai_identifier":"oai:kuscholarworks.ku.edu:1808/38065"},"canonical_url":"https://search.dev.ndltd.org/etd/ku/oai:kuscholarworks.ku.edu:1808/38065","repository":{"repo_id":"ku","name":"University of Kansas","base_url":"https://kuscholarworks.ku.edu/server/oai/request"},"display":{"title":"The Chromatic MacMahon Function","abstract":"We examine colorings of weighted graphs. Firstly, we examine the weighted analogue of Stanley’s chromatic symmetric function, and prove that the weighted analogue of Crew’s conjecture is not true. Secondly, we generalize the chromatic symmetric function to the chromatic MacMahon function, and use that to prove the MacMahon analogue of Crew’s conjecture.","abstract_html":"We examine colorings of weighted graphs. Firstly, we examine the weighted analogue of Stanley’s chromatic symmetric function, and prove that the weighted analogue of Crew’s conjecture is not true. Secondly, we generalize the chromatic symmetric function to the chromatic MacMahon function, and use that to prove the MacMahon analogue of Crew’s conjecture.","abstract_has_math":false,"creators":["Trist, May Bee"],"institution":"University of Kansas","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Martin, Jeremy L."],"committee_chairs":[],"committee_members":[],"year":2025,"date_issued":"2025-05-31","date_published":"2025-05-31","updated_at":"2026-07-24T02:47:27Z","subjects":["Mathematics","Combinatorics","Graph Theory","Symmetric Functions"],"languages":["en"],"rights":["This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["https://www.proquest.com/LegacyDocView/DISSNUM/32042898"],"render_values":[{"text":"https://www.proquest.com/LegacyDocView/DISSNUM/32042898","href":"https://www.proquest.com/LegacyDocView/DISSNUM/32042898","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/1808/38065","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Martin, Jeremy L."]},{"key":"dc:creator","label":"Author","values":["Trist, May Bee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2026-04-22T19:39:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2026-04-22T19:39:11Z"]},{"key":"dc:date.issued","label":"Date","values":["2025-05-31"]},{"key":"dc:publisher","label":"Institution","values":["University of Kansas"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics","Combinatorics","Graph Theory","Symmetric Functions"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["https://www.proquest.com/LegacyDocView/DISSNUM/32042898"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/1808/38065"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We examine colorings of weighted graphs. Firstly, we examine the weighted analogue of Stanley’s chromatic symmetric function, and prove that the weighted analogue of Crew’s conjecture is not true. Secondly, we generalize the chromatic symmetric function to the chromatic MacMahon function, and use that to prove the MacMahon analogue of Crew’s conjecture."]},{"key":"dc:title","label":"Title","values":["The Chromatic MacMahon Function"]}]}],"canonical_facts":{"dc:contributor.advisor":["Martin, Jeremy L."],"dc:creator":["Trist, May Bee"],"dc:date.accessioned":["2026-04-22T19:39:11Z"],"dc:date.available":["2026-04-22T19:39:11Z"],"dc:date.issued":["2025-05-31"],"dc:description.abstract":["We examine colorings of weighted graphs. Firstly, we examine the weighted analogue of Stanley’s chromatic symmetric function, and prove that the weighted analogue of Crew’s conjecture is not true. Secondly, we generalize the chromatic symmetric function to the chromatic MacMahon function, and use that to prove the MacMahon analogue of Crew’s conjecture."],"dc:identifier.other":["https://www.proquest.com/LegacyDocView/DISSNUM/32042898"],"dc:identifier.uri":["https://hdl.handle.net/1808/38065"],"dc:language.iso":["en"],"dc:publisher":["University of Kansas"],"dc:rights":["This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author."],"dc:subject":["Mathematics","Combinatorics","Graph Theory","Symmetric Functions"],"dc:title":["The Chromatic MacMahon Function"],"dc:type":["Thesis"]},"updated_at":"2026-07-24T02:47:27Z"}