In [the paper](http://arxiv.org/pdf/1512.08113.pdf), cluster algebra structures on $Gr(2,n)$, $Gr(3,6)$, $Gr(3,7)$, $Gr(3,8)$, $Gr(4,6)$ are described. But what are the cluster algebra structures on $Gr(3,5)$ (and $Gr(3,4)$)? Do we have cluster algebra structure on $Gr(2,3)$ and $Gr(2,4)$? Thank you very much.



What are the cluster algebra structures on $Gr(3,5)$?
The canonical source for the cluster structure on (all) Grassmannians is the aptly-titled


*Joshua S. Scott*, MR 2205721 [**Grassmannians and cluster algebras**](http://dx.doi.org/10.1112/S0024611505015571), *Proc. London Math. Soc. (3)* **92** (2006), no. 2, 345--380.


More information can also be found in papers citing this one.


