Some relations on Miyazawa's virtual knot invariant
Kauffman defined a polynomial invariant \(f_{L}(A)\in{\mathbb Z}[A^2,A^{-2}]\) for a virtual link \(L\) [\textit{L. H. Kauffman}, Eur. J. Comb. 20, No.~7, 663--690 (1999; Zbl 0938.57006)]. The Miyazawa polynomial \(R_{L}(A,h)\in{\mathbb Z}[A,A^{-1},h]\) is a 2-variable polynomial invariant for virtual links [\textit{N. Kamada} and \textit{Y. Miyazawa}, Hiroshima Math. J. 35, No.~2, 309--326 (2005; Zbl 1093.57007)]. It is equal to \(f_{L}(A)\) after substituting \(1\) for \(h\). In the paper under discussion the author introduces a relation between the Miyazawa polynomials of links in a virtual skein triple. This generalizes results from [\textit{N. Kamada}, Osaka J. Math. 39, No.~2, 325--333 (2002; Zbl 1007.57005)] and [\textit{N. Kamada, S. Nakabo} and \textit{S. Satoh}, Ill. J. Math. 46, No.~2, 467--475 (2002; Zbl 1008.57007)].
scientific article; zbMATH DE number 5144529