Pure Math Graduate Student Conference

Abstract

"A family of Spectrally Arbitrary Zero-Nonzero"

Spectrally arbitrary patterns have become of interest in the past decade. Work has been accomplished in classifying 4x4 and 5x5 spectrally arbitrary zero-nonzero patterns as well as families of nxn minimally spectrally arbitrary patterns. The most common method of proof is implementing the Nilpotent Jacobian method developed by Britz, McDonald, Olesky, and Van Den Driessche in Minimal Spectrally Arbitrary Sign Patterns. In this talk we will use the Nilpotent Jacobian method to establish the necessary conditions needed for a nxn irreducible zero-nonzero pattern with \frac{n(n+1)}{2}+1 nonzero entries, at least two of which lie on the diagonal, and at least two transversals to be spectrally arbitrary.