Bounds on the local bases of primitive nonpowerful nearly reducible sign patterns

Authors: Gao, Yubin¹; Shao, Yanling¹; Shen, Jian²

Source: Linear and Multilinear Algebra, Volume 57, Number 2, January 2009 , pp. 205-215(11)

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Abstract:

In this work, we study the kth local base, which is a generalization of the base, of a primitive non-powerful nearly reducible sign pattern of order n ≥ 7. We obtain the sharp bound together with a complete characterization of the equality case, of the kth local bases for primitive non-powerful nearly reducible sign patterns. We also show that there exist “gaps” in the kth local base set of primitive non-powerful nearly reducible sign patterns.

Keywords: sign pattern; nearly reducible; primitive; powerful; local base

Document Type: Research article

DOI: http://dx.doi.org/10.1080/03081080701763433

Affiliations: 1: Department of Mathematics, North University of China, Taiyuan, Shanxi 030051, P.R. China 2: Department of Mathematics, Texas State University, San Marcos, TX 78666, USA

Publication date: 2009-01-01