Computing Indexes and Periods of All Boolean Matrices Up to Dimension n=8 - Zajac, Pavol; Jokay, Matus (Computing and Informatics, 2013)
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.