$Y$ -meshes and generalized pentagram maps

Abstract

We introduce a rich family of generalizations of the pentagram map sharing the property that each generates an infinite configuration of points and lines with four points on each line. These systems all have a description as $Y$ -mutations in a cluster algebra and hence establish new connections between cluster theory and projective geometry.

Keywords

• pentagram map
• discrete dynamical systems
• cluster algebras
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]