The external vertices conjecture in case n=4

Abstract

The determinantal conjecture of M. Marcus and G.N. de Oliveira is known is many special cases. The case of 3 x 3 matrices was settled by N. Bebiano, J.K. Merikoski and J. da Providencia. The case n=4 remains open. In this article a technical conjecture is established implying a weakened form of the dereminantal conjecture for n=4.