English

The multivariate signed Bollobas-Riordan polynomial

Combinatorics 2009-10-23 v2

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.

Keywords

Cite

@article{arxiv.0811.1584,
  title  = {The multivariate signed Bollobas-Riordan polynomial},
  author = {Fabien Vignes-Tourneret},
  journal= {arXiv preprint arXiv:0811.1584},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T11:40:09.303Z