The multivariate signed Bollobas-Riordan polynomial

Details The multivariate signed Bollobas-Riordan polynomial The multivariate signed Bollobas-Riordan polynomial

2008-11-11

arxiv.org/abs/0811.1584v2

Discrete Mathematics, 309:5968-5981, 2009

Mathematics

Combinatorics

17 pages, 2 figures. Published version: a section added about the quasi-tree expansion of the multivariate Bollobas-Riordan po

Scientific paper

10.1016/j.disc.2009.04.026

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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