Authors: | Stošić, Marko | Title: | New categorifications of the chromatic and dichromatic polynomials for graphs | Journal: | Fundamenta Mathematicae | Volume: | 190 | First page: | 231 | Last page: | 243 | Issue Date: | 5-Jul-2006 | Rank: | M22 | ISSN: | 0016-2736 | DOI: | 10.4064/fm190-0-9 | Abstract: | For each graph G, we define 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 define 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 categorifications of the HOMFLYPT polynomial. We also give a simplified definition of this triply-graded link homology theory. |
Keywords: | Chromatic polynomial | Dichromatic polynomial | Graph | Homology | Khovanov-Rozansky | Koszul complex | Publisher: | Instytut Matematyczny Polskiej Akademii Nauk | Project: | FCT, Grant no. SFRH/BD/6783/2001 |
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