Permutation Matrices and Matrix Equivalence Over a Finite Field

Gary L. Mullen

doi:10.1155/S0161171281000367

Permutation Matrices and Matrix Equivalence Over a Finite Field

Gary L. Mullen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let F = GF(q) denote the finite field of order q and F_m×n the ring of m × n matrices over F. Let P_n be the set of all permutation matrices of order n over F so that P_n is ismorphic to S_n. If Ω is a subgroup of P_n and A, BɛF_m×n then A is equivalent to B relative to Ω if there exists ΡεΡ_n such that AP = B. In sections 3 and 4, if Ω = P_n, 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.

Original language	English (US)
Pages (from-to)	503-512
Number of pages	10
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	4
Issue number	3
DOIs	https://doi.org/10.1155/S0161171281000367
State	Published - 1981

All Science Journal Classification (ASJC) codes

Mathematics (miscellaneous)

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10.1155/S0161171281000367

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AB - Let F = GF(q) denote the finite field of order q and Fm×n the ring of m × n matrices over F. Let Pn be the set of all permutation matrices of order n over F so that Pn is ismorphic to Sn. If Ω is a subgroup of Pn and A, BɛFm×n then A is equivalent to B relative to Ω if there exists ΡεΡn such that AP = B. In sections 3 and 4, if Ω = Pn, 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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Permutation Matrices and Matrix Equivalence Over a Finite Field

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