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/

Zendy Plus

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

Zendy Tools

Zendy Open

Double Hurwitz numbers have at least four equivalent definitions. Mostnaturally, they count covers of the Riemann sphere by genus g curves withcertain specified ramification data. This is classically equivalent to countingcertain collections of permutations. More recently, double Hurwitz numbers havebeen expressed as a count of certain ribbon graphs, or as a weighted count ofcertain labeled graphs.  This note is an expository account of the equivalences between thesedefinitions, with a few novelties. In particular, we give a simplecombinatorial algorithm to pass directly between the permutation and ribbongraph definitions. The two graph theoretic points of view have been used togive proofs that double Hurwitz numbers are piecewise polynomial. We use ouralgorithm to compare these two proofs.

Hurwitz numbers, ribbon graphs, and tropicalization