Matrices of inversions for permutations: Recognition and Applications - Elrifai, E. A.; Alghamdi, Redha. A. (JOURNAL OF ADVANCES IN MATHEMATICS, 2014)
This work provides a criterion for a binary strictly upper triangle matrices to be a matrix of inversions for a permutation. It admits an invariant matrices for permutations to being well recognizable. Then it provides a complete algorithmic classi…cation of elements in the symmetric group Sn. Also it gives an algorithm for generating and writing a permutation in a unique canonical form, as a word of transpositions.