New categorifications of the chromatic and dichromatic polynomials for graphs

Marko Stošić

Fundamenta Mathematicae (2006)

  • Volume: 190, Issue: 1, page 231-243
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Marko Stošić. "New categorifications of the chromatic and dichromatic polynomials for graphs." Fundamenta Mathematicae 190.1 (2006): 231-243. <http://eudml.org/doc/282963>.

@article{MarkoStošić2006,
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.},
author = {Marko Stošić},
journal = {Fundamenta Mathematicae},
keywords = {graph; homology; chromatic polynomial; dichromatic polynomial; Koszul complex; Khovanov-Rozansky categorification},
language = {eng},
number = {1},
pages = {231-243},
title = {New categorifications of the chromatic and dichromatic polynomials for graphs},
url = {http://eudml.org/doc/282963},
volume = {190},
year = {2006},
}

TY - JOUR
AU - Marko Stošić
TI - New categorifications of the chromatic and dichromatic polynomials for graphs
JO - Fundamenta Mathematicae
PY - 2006
VL - 190
IS - 1
SP - 231
EP - 243
AB - 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.
LA - eng
KW - graph; homology; chromatic polynomial; dichromatic polynomial; Koszul complex; Khovanov-Rozansky categorification
UR - http://eudml.org/doc/282963
ER -

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