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

We extend the duality between acyclic orientations and totally cyclicorientations on planar graphs to dualities on graphs on orientable surfaces byintroducing boundary acyclic orientations and totally bi-walkable orientations.In addition, we provide a reciprocity theorem connecting local tensions andboundary acyclic orientations. Furthermore, we define the balanced flowpolynomial which is connected with tension polynomial by duality and withtotally bi-walkable orientations by reciprocity.

Dualities and reciprocities on graphs on surfaces