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math.GN2019
Cayley Graphs on Billiard Surfaces, and Their Genus
Jason Schmurr, Jaime Lynne McCartney, Joanna Grzegrzolka
In this article we discuss a connection between two famous constructions in mathematics: a Cayley graph of a group and a (rational) billiard surface. For each rational billiard sur…
math.GN2008
Translation Covers Among Triangular Billiard Surfaces
Jason Schmurr
We identify all translation covers among triangular billiard surfaces. Our main tools are the holonomy field of Kenyon and Smillie and a geometric property of translation surfaces,…