Upper Bounds for the Isolation Number of a Matrix over Semirings

LeRoy B. Beasley and Seok-Zun Song
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LeRoy B. Beasley: Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA
Seok-Zun Song: Department of Mathematics, Jeju National University, Jeju 63243, Korea

Mathematics, 2019, vol. 7, issue 1, 1-6

Abstract: Let S be an antinegative semiring. The rank of an m × n matrix B over S is the minimal integer r such that B is a product of an m × r matrix and an r × n matrix. The isolation number of B is the maximal number of nonzero entries in the matrix such that no two entries are in the same column, in the same row, and in a submatrix of B of the form b i , j b i , l b k , j b k , l with nonzero entries. We know that the isolation number of B is not greater than the rank of it. Thus, we investigate the upper bound of the rank of B and the rank of its support for the given matrix B with isolation number h over antinegative semirings.

Keywords: rank; Boolean rank; isolated entry; isolation number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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