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Discrete Seminar

POT 745
Speaker(s) / Presenter(s):
Zach Peterson

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.

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