Bases of primitive nonpowerful sign patterns

  • Authors:

  • Guanglong Yu;Zhengke Miao;Jinlong Shu

  • Affiliations:

  • Department of Mathematics, East China Normal University, Shanghai, China and Department of Mathematics, Xuzhou Normal University, Xuzhou, China;Department of Mathematics, Xuzhou Normal University, Xuzhou, China;Department of Mathematics, East China Normal University, Shanghai, China

  • Venue:
  • COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
  • Year:
  • 2010

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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 Al 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 3/2n2 - 2n + 4 is given. Some sign pattern matrices with given bases is characterized and some "gaps" in the base set are shown.