A Noncommutative Chromatic Symmetric Function

dc.creatorGebhard, David D.
dc.creatorSagan, Bruce E.
dc.date1999-07-12
dc.date.accessioned2026-07-07T05:29:52Z
dc.date.available2026-07-07T05:29:52Z
dc.descriptionStanley associated with a graph G a symmetric function X_G which reduces to G's chromatic polynomial under a certain specialization of variables. He then proved various theorems generalizing results about the chromatic polynomial, as well as new ones that cannot be interpreted at that level. Unfortunately, X_G does not satisfy a Deletion-Contraction Law which makes it difficult to apply induction. We introduce a symmetric function in noncommuting variables which does have such a law and specializes to X_G when the variables are allowed to commute. This permits us to further generalize some of Stanley's theorems and prove them in a uniform and straightforward manner. Furthermore, we make some progress on the (3+1)-free Conjecture of Stanley and Stembridge.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/math/9907076
dc.identifierhttp://arxiv.org/abs/math/9907076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78811
dc.subjectCombinatorics
dc.subject05C15
dc.titleA Noncommutative Chromatic Symmetric Function
dc.typetext

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