Computing Indexes and Periods of All Boolean Matrices Up to Dimension n=8

Year, pages: 2012, 1329 - 1344

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  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.

Zajac, P., Jókay, M. 2012. Computing Indexes and Periods of All Boolean Matrices Up to Dimension n=8. In Computing and Informatics, vol. 31, no.6, pp. 1329-1344. 1335-9150.

Zajac, P., Jókay, M. (2012). Computing Indexes and Periods of All Boolean Matrices Up to Dimension n=8. Computing and Informatics, 31(6), 1329-1344. 1335-9150.