The pentagram map and Y-patterns

Abstract

The pentagram map, introduced by R. Schwartz, is defined by the following construction: given a polygon as input, draw all of its "shortest" diagonals, and output the smaller polygon which they cut out. We employ the machinery of cluster algebras to obtain explicit formulas for the iterates of the pentagram map.

arXiv comment27 pages, 11 figures. To appear in Advances in Mathematics