2018/08/01 by Quang-Nhat Le, Le, Quang-Nhat
Mathematics · Physics and Astronomy · #Geometric and Algebraic Topology #Advanced Differential Equations and Dynamical Systems #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1808.00146
In a recent paper, Cristofaro-Gardiner--Li--Stanley [CGLS15] constructed examples of irrational triangles whose Ehrhart functions (i.e. lattice-point count) are polynomials when restricted to positive integer dilation factors. This is very surprising because the Ehrhart functions of rational polygons are usually only quasi-polynomials. We demonstrate that most of their triangles can also be obtained by a simple cut-and-paste procedure that allows us to build new examples with more sides. Our examples might potentially have applications in the theory of symplectic embeddings.