Circulant Boolean relation matrices

Štefan Schwarz

Displaying similar documents to “Circulant Boolean relation matrices”

A generalization of a theorem of Boolean relation matrices

Chong-Yun Chao, Shmuel Winograd (1977)

Czechoslovak Mathematical Journal

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Generalized indices of Boolean matrices

Bo Zhou (2002)

Czechoslovak Mathematical Journal

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We obtain upper bounds for generalized indices of matrices in the class of nearly reducible Boolean matrices and in the class of critically reducible Boolean matrices, and prove that these bounds are the best possible.

A combinatorial problem arising in finite Markov chains

Štefan Schwarz (1986)

Mathematica Slovaca

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The primitive Boolean matrices with the second largest scrambling index by Boolean rank

Yan Ling Shao, Yubin Gao (2014)

Czechoslovak Mathematical Journal

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The scrambling index of an $n \times n$ primitive Boolean matrix $A$ is the smallest positive integer $k$ such that $A^{k} {(A^{T})}^{k} = J$ , where $A^{T}$ denotes the transpose of $A$ and $J$ denotes the $n \times n$ all ones matrix. For an $m \times n$ Boolean matrix $M$ , its Boolean rank $b (M)$ is the smallest positive integer $b$ such that $M = A B$ for some $m \times b$ Boolean matrix $A$ and $b \times n$ Boolean matrix $B$ . In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an $n \times n$ primitive matrix $M$ in terms of its Boolean rank $b (M)$ , and they also characterized...