The pentagram map and Y-patterns

Details The pentagram map and Y-patterns The pentagram map and Y-patterns

2010-05-04

arxiv.org/abs/1005.0598v2

Mathematics

Combinatorics

27 pages, 11 figures. To appear in Advances in Mathematics

Scientific paper

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.

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