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dc.contributor.advisorMartin, Jeremy L
dc.contributor.authorHumpert, Brandon Eugene
dc.date.accessioned2011-06-21T18:46:33Z
dc.date.available2011-06-21T18:46:33Z
dc.date.issued2011-04-26
dc.date.submitted2011
dc.identifier.otherhttp://dissertations.umi.com/ku:11486
dc.identifier.urihttp://hdl.handle.net/1808/7662
dc.description.abstractWe study colorings and orientations of graphs in two related contexts. Firstly, we generalize Stanley's chromatic symmetric function using the k-balanced colorings of Pretzel to create a new graph invariant. We show that in fact this invariant is a quasisymmetric function which has a positive expansion in the fundamental basis. We also define a graph invariant generalizing the chromatic polynomial for which we prove some theorems analogous to well-known theorems about the chromatic polynomial. Secondly, we examine graphs and graph colorings in the context of the combinatorial Hopf algebras of Aguiar, Bergeron and Sottile. By doing so, we are able to obtain a new formula for the antipode of a Hopf algebra on graphs previously studied by Schmitt. We also obtain new interpretations of evaluations of the Tutte polynomial.
dc.format.extent84 pages
dc.language.isoen
dc.publisherUniversity of Kansas
dc.rightsThis item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
dc.subjectMathematics
dc.titlePolynomials associated with graph coloring and orientations
dc.typeDissertation
dc.contributor.cmtememberBayer, Margaret
dc.contributor.cmtememberHuneke, Craig
dc.contributor.cmtememberStahl, Saul
dc.contributor.cmtememberAlexander, Perry
dc.thesis.degreeDisciplineMathematics
dc.thesis.degreeLevelPh.D.
kusw.oastatusna
kusw.oapolicyThis item does not meet KU Open Access policy criteria.
dc.rights.accessrightsopenAccess


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