ELA, Volume 16, pp. 30-43, January 2007, abstract.

Inertially arbitrary nonzero patterns of order 4

Michael S. Cavers and Kevin N. Vander Meulen

Inertially arbitrary nonzero patterns of order at most 
4 are characterized. Some of these patterns are demonstrated
to be inertially arbitrary but not spectrally arbitrary. 
The order 4 sign patterns which are inertially arbitrary 
and have a nonzero pattern that is not spectrally arbitrary 
are also described. There exists an irreducible nonzero 
pattern which is inertially arbitrary but has no signing 
that is inertially arbitrary. In fact, up to equivalence, 
this pattern is unique among the irreducible order 4 patterns 
with this property.