Polygon recutting as a cluster integrable system
Exactly Solvable and Integrable Systems
2022-11-22 v3 Combinatorics
Dynamical Systems
Metric Geometry
Abstract
Recutting is an operation on planar polygons defined by cutting a polygon along a diagonal to remove a triangle, and then reattaching the triangle along the same diagonal but with opposite orientation. Recuttings along different diagonals generate an action of the affine symmetric group on the space of polygons. We show that this action is given by cluster transformations and is completely integrable. The integrability proof is based on interpretation of recutting as refactorization of quaternionic polynomials.
Cite
@article{arxiv.2201.12503,
title = {Polygon recutting as a cluster integrable system},
author = {Anton Izosimov},
journal= {arXiv preprint arXiv:2201.12503},
year = {2022}
}
Comments
20 pages, 6 figures; final version to appear in Selecta Math