New categorifications of the chromatic and dichromatic polynomials for graphs

• Autorzy: Marko Stošić
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57M25: Knots and links in S 3

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 190
• Numer: 1
• Strony: 231-243

Daty

wydano

2006

Twórcy

autor

Marko Stošić

• Departamento de Matemática and, CEMAT-Centro de Matemática e Aplicações, Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal

Identyfikatory

DOI

10.4064/fm190-0-9