Generalized indices of Boolean matrices

Bo Zhou

Displaying similar documents to “Generalized indices of Boolean matrices”

A combinatorial problem arising in finite Markov chains

Štefan Schwarz (1986)

Mathematica Slovaca

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Circulant Boolean relation matrices

Štefan Schwarz (1974)

Czechoslovak Mathematical Journal

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A generalization of a theorem of Boolean relation matrices

Chong-Yun Chao, Shmuel Winograd (1977)

Czechoslovak Mathematical Journal

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Power indices of trace zero symmetric Boolean matrices

Bo Zhou (2004)

Discussiones Mathematicae - General Algebra and Applications

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The power index of a square Boolean matrix A is the least integer d such that Ad is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n×n primitive symmetric Boolean matrices of trace zero, the class of n×n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zero, and characterize the extreme matrices respectively.

Boolean matrices ... neither Boolean nor matrices

Gabriele Ricci (2000)

Discussiones Mathematicae - General Algebra and Applications

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Boolean matrices, the incidence matrices of a graph, are known not to be the (universal) matrices of a Boolean algebra. Here, we also show that their usual composition cannot make them the matrices of any algebra. Yet, later on, we "show" that it can. This seeming paradox comes from the hidden intrusion of a widespread set-theoretical (mis) definition and notation and denies its harmlessness. A minor modification of this standard definition might fix it.

Some Fixed Point Theorems in Boolean Algebra

Koriolan Gilezan (1980)

Publications de l'Institut Mathématique

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Maximum exponent of Boolean circulant matrices with constant number of nonzero entries in their generating vector.

Bueno, M.I., Furtado, S., Sherer, N. (2009)

The Electronic Journal of Combinatorics [electronic only]

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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...