Let V be a k-dimensional complex vector space. The Plücker ring of polynomial SL(V ) invariants of a collection of n vectors in V can be alternatively described as the homogeneous coordinate ring of the Grassmannian Gr(k, n). In 2003, using combinatorial tools developed by A. Postnikov, J. Scott showed that the Plücker ring carries a cluster algebra structure. Over the ensuing decade, this has ...