Zero-nonzero tree patterns that allow Sn∗
Luyining Gan, Wei Gao, Jie Han · Linear and Multilinear Algebra · 2021
For n≥2, let Sn∗={(0,n,0),(0,n−1,1),(1,n−1,0),(n,0,0),(n−1,0,1),(n−1,1,0)}. A zero-nonzero pattern A of order n allows Sn∗ if Sn∗⊆i(A), the inertia set of A, and requires Sn∗ if Sn∗=i(A). The study of zero-nonzero patterns allowing Sn∗ was introduced by Berliner et al. [Inertia sets allowed by matrix patterns. Electron J Linear Algebra. 2018;34:343–355]. In this paper, we give characterizations of irreducible zero-nonzero path patterns and double-star patterns that allow Sn∗. Moreover, all irreducible zero-nonzero tree patterns of order 5 and 6 that allow Sn∗ are also characterized.