Constructs doubly- and triply-graded Penrose-type homologies for ribbon graphs via TQFT cube of resolutions whose Euler characteristics recover Penrose polynomial specializations.
A categorification for the chromatic polynomial
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abstract
For each graph we construct graded cohomology groups whose graded Euler characteristic is the chromatic polynomial of the graph. We show the cohomology groups satisfy a long exact sequence which corresponds to the well-known deletion-contraction rule. This work is motivated by Khovanov's work on categorification of the Jones polynomial of knots.
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math.CO 1years
2026 1verdicts
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Categorification of some Penrose polynomials
Constructs doubly- and triply-graded Penrose-type homologies for ribbon graphs via TQFT cube of resolutions whose Euler characteristics recover Penrose polynomial specializations.