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 give a combinatorial interpretation for certain cluster variables inGrassmannian cluster algebras in terms of double and triple dimerconfigurations. More specifically, we examine several Gr(3,n) cluster variablesthat may be written as degree two or degree three polynomials in terms ofPl\"ucker coordinates, and give generating functions for their images under thetwist map - a cluster algebra automorphism introduced in work ofBerenstein-Fomin-Zelevinsky. The generating functions range over certain doubleor triple dimer configurations on an associated plabic graph, which we describeusing particular non-crossing matchings or webs (as defined by Kuperberg),respectively. These connections shed light on a recent conjecture of Cheung etal., extend the concept of web duality introduced in a paper of Fomin-Lam-Le,and more broadly make headway on understanding Grassmannian cluster algebrasfor Gr(3,n).

Twists of Gr(3,n) Cluster Variables as Double and Triple Dimer Partition Functions