Ber-Lin Yu and Ting-Zhu Huang Minimal Critical Sets of Inertias for Irreducible Zerononzero Patterns of Order 3
127 - 129
2010
4
1
International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering http://waset.org/publications/11586
http://waset.org/publications/37
World Academy of Science, Engineering and Technology
If there exists a nonempty, proper subset S of the set of all (n 1)(n 2)2 inertias such that S Ôèå i(A) is sufficient for any n × n zerononzero pattern A to be inertially arbitrary, then S is called a critical set of inertias for zerononzero patterns of order n. If no proper subset of S is a critical set, then S is called a minimal critical set of inertias. In 3, Kim, Olesky and Driessche identified all minimal critical sets of inertias for 2 × 2 zerononzero patterns. Identifying all minimal critical sets of inertias for n × n zerononzero patterns with n ≥ 3 is posed as an open question in 3. In this paper, all minimal critical sets of inertias for 3 × 3 zerononzero patterns are identified. It is shown that the sets (0, 0, 3), (3, 0, 0), (0, 0, 3), (0, 3, 0), (0, 0, 3), (0, 1, 2), (0, 0, 3), (1, 0, 2), (0, 0, 3), (2, 0, 1) and (0, 0, 3), (0, 2, 1) are the only minimal critical sets of inertias for 3 × 3 irreducible zerononzero patterns.
International Science Index 37, 2010