Gary L. Mullen, "Permutation matrices and matrix equivalence over a finite field", International Journal of Mathematics and Mathematical Sciences, vol. 4, Article ID 583823, 10 pages, 1981. https://doi.org/10.1155/S0161171281000367
Permutation matrices and matrix equivalence over a finite field
Let denote the finite field of order and the ring of matrices over . Let be the set of all permutation matrices of order over so that is ismorphic to . If is a subgroup of and , then is equivalent to relative to if there exists such that . In sections 3 and 4, if formulas are given for the number of equivalence classes of a given order and for the total number of classes. In sections 5 and 6 we study two generalizations of the above definition.
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