Non-orientable quasi-trees for the Bollobas-Riordan polynomial

Details Non-orientable quasi-trees for the Bollobas-Riordan polynomial Non-orientable quasi-trees for the Bollobas-Riordan polynomial

2011-02-08

arxiv.org/abs/1102.1627v1

Europ. J. Comb., 32:510-532, 2011

Mathematics

Combinatorics

31 pages, 11 figures

Scientific paper

10.1016/j.ejc.2010.12.005

We extend the quasi-tree expansion of A. Champanerkar, I. Kofman, and N. Stoltzfus to not necessarily orientable ribbon graphs. We study the duality properties of the Bollobas-Riordan polynomial in terms of this expansion. As a corollary, we get a "connected state" expansion of the Kauffman bracket of virtual link diagrams. Our proofs use extensively the partial duality of S. Chmutov.

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