Computing Indexes and Periods of All Boolean Matrices Up to Dimension n=8
Pavol Zajac; Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Informatics, Slovak Technical University in Bratislava ; Matus Jokay; Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Informatics, Slovak Technical University in Bratislava
Computing and Informatics, Tome 31 (2013) no. 6, / Harvested from Computing and Informatics
Text on Computing and Informatics
A set of n x n Boolean matrices along with the Boolean matrix multiplication operation form a semigroup. For each matrix A it is possible to find index r and period  , such that A, = A ++ and  , , are the smallest positive integers with this property. We are concerned with a question: How many n times n Boolean matrices have the given index, and period? A new algorithm is presented that was used to compute index and period statistics of all square Boolean matrices up to n=8. Computed statistics are presented in the appendix of the paper.
Publié le : 2013-01-24
Classification:  Boolean matrix, enumeration, directed graphs 
@article{cai1310,
     author = {Pavol Zajac; Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Informatics, Slovak Technical University in Bratislava and Matus Jokay; Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Informatics, Slovak Technical University in Bratislava},
     title = {Computing Indexes and Periods of All Boolean Matrices Up to Dimension n=8},
     journal = {Computing and Informatics},
     volume = {31},
     number = {6},
     year = {2013},
     language = {en},
     url = {http://dml.mathdoc.fr/item/cai1310}
}

Pavol Zajac; Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Informatics, Slovak Technical University in Bratislava; Matus Jokay; Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Informatics, Slovak Technical University in Bratislava. Computing Indexes and Periods of All Boolean Matrices Up to Dimension n=8. Computing and Informatics, Tome 31 (2013) no. 6, . http://gdmltest.u-ga.fr/item/cai1310/