Title: Combinatorics of Conway-Coxeter Friezes and SL_k-Tilings
Abstract: In 1973, Conway and Coxeter published an article which introduced objects called friezes. In it they detailed several structural properties of these objects, including a bijection to triangulations of polygons. In more recent years, these Conway-Coxeter friezes and their higher-dimensional analogues known as SL_k-tilings have been studied due to their relation to cluster algebras. Tilings are arrays of integers whose adjacent submatrices have determinant 1. In the case of SL_2-tilings, there is a bijection to paths in the Farey Graph. We prove that for higher k there is a bijection to certain sequences of k-vectors.