Abstract
For a square primitive nonpowerful sign pattern A, the base of A, denoted by l(A), is the least positive integer l such that every entry of A l is #. In this paper, we consider the base set of the primitive nonpowerful sign pattern matrices. Some bounds on the bases for the sign pattern matrices with base at least \(\displaystyle \frac{3}{2}n^{2}-2n+4\) is given. Some sign pattern matrices with given bases is characterized and some “gaps” in the base set are shown.
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Yu, G., Miao, Z., Shu, J. (2010). Bases of Primitive Nonpowerful Sign Patterns. In: Wu, W., Daescu, O. (eds) Combinatorial Optimization and Applications. COCOA 2010. Lecture Notes in Computer Science, vol 6508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17458-2_11
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DOI: https://doi.org/10.1007/978-3-642-17458-2_11
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