New Categorifications of the Chromatic and the Dichromatic Polynomials for Graphs

Details New Categorifications of the Chromatic and the Dichromatic Polynomials for Graphs New Categorifications of the Chromatic and the Dichromatic Polynomials for Graphs

2005-07-14

arxiv.org/abs/math/0507290v2

Fund. Math. 190 (2006), 231-243

Mathematics

Quantum Algebra

15 pages, added Section 2

Scientific paper

In 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.

Affiliated with

Also associated with

No associations

Rating

New Categorifications of the Chromatic and the Dichromatic Polynomials for Graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with New Categorifications of the Chromatic and the Dichromatic Polynomials for Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and New Categorifications of the Chromatic and the Dichromatic Polynomials for Graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-575480