Zero-nonzero tree patterns that allow Sn*.

For n ≥ 2, let S 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. [ABSTRACT FROM AUTHOR]