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A Preliminary Study on the Eventual Positivity of Irreducible Tridiagonal Sign Patterns

Motivated by Berman et al. [Sign patterns that allow eventual positivity, ELA, 19(2010): 108-120], we concentrate on the potential eventual positivity of irreducible tridiagonal sign patterns. The minimal potential eventual positivity of irreducible tridiagonal sign patterns of order less than six is established, and all the minimal potentially eventually positive tridiagonal sign patterns of order ≤ 5 are identified. Our results indicate that if an irreducible tridiagonal sign pattern of order less than six A is minimal potentially eventually positive, then A requires the eventual positivity. Keywords—eventual positivity, potentially positive sign pattern, tridiagnoal sign pattern, minimal potentially positive sign pattern.