The cable Γ-polynomials of mutant knots

The Γ-polynomial is an invariant of an oriented link in the 3-sphere, which is the common zeroth coefficient polynomial of both the HOMFLYPT and Kauffman polynomials. It is known that the HOMFLYPT and Kauffman polynomials, their 2-cable versions, and the satellite versions of the Alexander and Jones polynomials are invariant under mutation. On the other hand, there exists a mutant knot pair which is distinguished by the 3-cable version of the HOMFLYPT polynomial. In this paper, we show that the 3-cable version of the Γ-polynomial is invariant under mutation.