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arXiv · 0811.1584

The multivariate signed Bollobas-Riordan polynomial

Fabien Vignes-Tourneret
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Abstract

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.

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Fabien Vignes-Tourneret. 2009-10-23. The multivariate signed Bollobas-Riordan polynomial. https://doi.org/10.1016/j.disc.2009.04.026

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