New Categorifications of the Chromatic and the Dichromatic Polynomials for Graphs

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dc.creatorStosic, Marko
dc.date2005-07-14
dc.date2006-05-22
dc.date.accessioned2026-07-07T06:42:37Z
dc.date.available2026-07-07T06:42:37Z
dc.descriptionIn this paper, for each graph $G$, we def\mbox{}ine a chain complex of graded modules over the ring of polynomials, whose graded Euler characteristic is equal to the chromatic polynomial of $G$. Furthermore, we def\mbox{}ine a chain complex of doubly-graded modules, whose (doubly) graded Euler characteristic is equal to the dichromatic polynomial of $G$. Both constructions use Koszul complexes, and are similar to the new Khovanov-Rozansky categorif\mbox{}ications of HOMFLYPT polynomial. We also give simplif\mbox{}ied def\mbox{}inition of this triply-graded link homology theory.
dc.description15 pages, added Section 2
dc.identifierhttps://arxiv.org/abs/math/0507290
dc.identifierhttp://arxiv.org/abs/math/0507290
dc.identifierFund. Math. 190 (2006), 231-243
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102110
dc.subjectQuantum Algebra
dc.subjectCombinatorics
dc.subject57M25
dc.titleNew Categorifications of the Chromatic and the Dichromatic Polynomials for Graphs
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