English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

It is well a known and fundamental result that the Jones polynomial can beexpressed as Potts and vertex partition functions of signed plane graphs. Herewe consider constructions of the Jones polynomial as state models of unsignedgraphs and show that the Jones polynomial of any link can be expressed as avertex model of an unsigned embedded graph.  In the process of deriving this result, we show that for every diagram of alink in the 3-sphere there exists a diagram of an alternating link in athickened surface (and an alternating virtual link) with the same Kauffmanbracket. We also recover two recent results in the literature relating theJones and Bollobas-Riordan polynomials and show they arise from two differentinterpretations of the same embedded graph.

Unsigned state models for the Jones polynomial