Circulant Boolean relation matrices

Kim Ki-Hang Butler; James Richard Krabill

Displaying similar documents to “Circulant Boolean relation matrices”

The Euler-Fermat theorem for the semigroup of circulant Boolean matrices

Štefan Schwarz (1980)

Czechoslovak Mathematical Journal

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On the maximal subgroup of the sandwich semigroup of generalized circulant Boolean matrices

Jinsong Chen, Yi Jia Tan (2006)

Czechoslovak Mathematical Journal

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Let $n$ be a positive integer, and $C_{n} (r)$ the set of all $n \times n$ $r$ -circulant matrices over the Boolean algebra $B = {0, 1}$ , $G_{n} = ⋃_{r = 0}^{n - 1} C_{n} (r)$ . For any fixed $r$ -circulant matrix $C$ ( $C \neq 0$ ) in $G_{n}$ , we define an operation “ $*$ ” in $G_{n}$ as follows: $A * B = A C B$ for any $A, B$ in $G_{n}$ , where $A C B$ is the usual product of Boolean matrices. Then $(G_{n}, *)$ is a semigroup. We denote this semigroup by $G_{n} (C)$ and call it the sandwich semigroup of generalized circulant Boolean matrices with sandwich matrix $C$ . Let $F$ be an idempotent element in $G_{n} (C)$ and $M (F)$ the maximal subgroup...