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For, let. A zero-nonzero patternof order  n  allowsif, the inertia set of, and requiresif. The study of zero-nonzero patterns allowingwas 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. Moreover, all irreducible zero-nonzero tree patterns of order 5 and 6 that alloware also characterized.

linear and multilinear algebra

Zero-nonzero tree patterns that allow                                                                                                    S                                                     n                           ∗