On characterization of a multivariable polynomial invariant of twisted links

Twisted link diagrams are a generalization of virtual link diagrams, which correspond to link diagrams on orientable or non-orientable surfaces. A multivariable polynomial invariant of a twisted link is a generalization of a multivariable polynomial invariant of a virtual link. In this paper, we give a characterization of a multivariable polynomial invariant of twisted links with some specific properties.