We show that the zeroth coefficient of the cables of the HOMFLY polynomial (colored HOMFLY polynomials) does not distinguish mutants. This makes a sharp contrast with the total HOMFLY polynomial whose 3-cables can distinguish mutants.
"Mutation invariance for the zeroth coefficients of colored HOMFLY polynomial." Kodai Math. J. 43 (1) 1 - 15, March 2020. https://doi.org/10.2996/kmj/1584345685