# What are the cluster algebra structures on $Gr(3,5)$?

In the paper, 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.

• $Gr(k,n) \cong Gr(n-k,n)$. – Sasha Sep 14 '16 at 14:55