### 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) |
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Pages (from-to) | 503-512 |

Number of pages | 10 |

Journal | International Journal of Mathematics and Mathematical Sciences |

Volume | 4 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1981 |

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### All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)

### Cite this

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**Permutation Matrices and Matrix Equivalence Over a Finite Field.** / Mullen, Gary L.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Permutation Matrices and Matrix Equivalence Over a Finite Field

AU - Mullen, Gary L.

PY - 1981/1/1

Y1 - 1981/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84956443866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84956443866&partnerID=8YFLogxK

U2 - 10.1155/S0161171281000367

DO - 10.1155/S0161171281000367

M3 - Article

AN - SCOPUS:84956443866

VL - 4

SP - 503

EP - 512

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

IS - 3

ER -