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Prime boolean matrices

Contributed Papers

Part of the Lecture Notes in Mathematics book series (LNM,volume 829)

Abstract

Let A, B, C be n×n matrices of zeros and ones. Using Boolean addition and multiplication, we say that A is prime if A is not a permutation matrix and if A=BC then B or C must be a permutation matrix. Sufficient conditions for A to be prime are given.

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References

  1. De de Caen, Prime Boolean Matrices, Master’s Thesis, Queen’s University at Kingston (1979).

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  2. J. Borosh, D.J. Hartfiel and C.J. Maxson, Answers to Questions posed by Richman and Schneider, Linear and Multilinear Algebra 3 (1976), 255–258.

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  3. D.J. Richman and H. Schneider, Primes in the Semigroup of Non-negative Matrices, Linear and Multilinear Algebra 2 (1974), 135–140.

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© 1980 Springer-Verlag

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De Caen, D., Gregory, D.A. (1980). Prime boolean matrices. In: Robinson, R.W., Southern, G.W., Wallis, W.D. (eds) Combinatorial Mathematics VII. Lecture Notes in Mathematics, vol 829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0088902

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  • DOI: https://doi.org/10.1007/BFb0088902

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10254-0

  • Online ISBN: 978-3-540-38376-5

  • eBook Packages: Springer Book Archive