New categorifications of the chromatic and dichromatic polynomials for graphs

Volume 190 / 2006

Marko Stošić Fundamenta Mathematicae 190 (2006), 231-243 MSC: Primary 57M25. 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.

Authors

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

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