Refined inertias of positive and hollow positive patterns
Refined inertias of positive and hollow positive patterns
Abstract We investigate refined inertias of positive patterns and patterns that have each off-diagonal entry positive and each diagonal entry zero, i.e., hollow positive patterns. For positive patterns, we prove that every refined inertia <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi>n</m:mi> </m:mrow> <m:mrow> <m:mo>+</m:mo> </m:mrow> </m:msub> <m:mo>,</m:mo> <m:msub> <m:mrow> …