The multivariate signed Bollobas-Riordan polynomial

Autor(en)

Fabien Vignes-Tourneret

Abstrakt

We generalise the signed Bollobás–Riordan polynomial of S. Chmutov and I. Pak [S. Chmutov, I. Pak, The Kauffman bracket of virtual links and the Bollobás–Riordan polynomial, Mos. Math. J. 7(3) (2007), 409–418] to a multivariate signed polynomial ZZ and study its properties. We prove the invariance of ZZ under the recently defined partial duality of S. Chmutov [S. Chmutov, Generalized duality for graphs on surfaces and the signed Bollobás–Riordan polynomial, J. Combin. Theory, Ser. B 99(3) (2009), 617–638. arXiv:0711.3490, doi:10.1016/j.jctb.2008.09.007] and show that the duality transformation of the multivariate Tutte polynomial is a direct consequence of it.

Organisation(en)

Mathematische Physik

Journal

Discrete Mathematics

Band

309

Seiten

5968-5981

Anzahl der Seiten

14

ISSN

0012-365X

DOI

https://doi.org/10.1016/j.disc.2009.04.026

Publikationsdatum

2009

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/3266a4dd-1b2e-49e0-91d7-1921ca6033bc