  We generalise the signed Bollobas-Riordan polynomial of S. Chmutov and I. Pak
[Moscow Math. J. 7 (2007), no. 3, 409-418] to a multivariate signed polynomial
Z and study its properties. We prove the invariance of Z under the recently
defined partial duality of S. Chmutov [J. Combinatorial Theory, Ser. B, 99 (3):
617-638, 2009] and show that the duality transformation of the multivariate
Tutte polynomial is a direct consequence of it.
