대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제56권2호
  • /
  • Pages.305-318
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  • 2019
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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POTENTIALLY EVENTUALLY POSITIVE BROOM SIGN PATTERNS

  • Yu, Ber-Lin (Faculty of Mathematics and Physics Huaiyin Institute of Technology)
  • 투고 : 2017.12.22
  • 심사 : 2019.03.04
  • 발행 : 2019.03.31
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초록

A sign pattern is a matrix whose entries belong to the set {+, -, 0}. An n-by-n sign pattern ${\mathcal{A}}$ is said to allow an eventually positive matrix or be potentially eventually positive if there exist at least one real matrix A with the same sign pattern as ${\mathcal{A}}$ and a positive integer $k_0$ such that $A^k>0$ for all $k{\geq}k_0$. Identifying the necessary and sufficient conditions for an n-by-n sign pattern to be potentially eventually positive, and classifying the n-by-n sign patterns that allow an eventually positive matrix are two open problems. In this article, we focus on the potential eventual positivity of broom sign patterns. We identify all the minimal potentially eventually positive broom sign patterns. Consequently, we classify all the potentially eventually positive broom sign patterns.

키워드

E1BMAX_2019_v56n2_305_f0001.png 이미지

FIGURE 1. The graph of broom sign patten B4,5.

참고문헌

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