Tuesday, February 21st, 2012
9:30am - 10:30am, in Campus Center 3-3540

Edward Richmond

University of British Columbia

A combinatorial characterization of tight fusion frames using Littlewood-Richardson coefficients

Abstract: A tight fusion frame is a sequence of orthogonal projection matrices that sums to a scalar multiple of the identity. Such sequences are used to model sensor networks and have applications in coding theory, neurology and compressed sensing. To any tight fusion frame, we can associate a sequence of positive integers given by the ranks of the matrices. We consider the following classification question: For which sequences of positive integers do tight fusion frames exist? In this talk, I will discuss joint work with K. Luoto and M. Bownik where we explore this problem. In particular, we give a combinatorial characterization in terms of non-vanishing Littlewood-Richardson coefficients. This connection between algebraic combinatorics and frame theory yields several interesting results in both fields of mathematics.