Permutation Matrices and Matrix Equivalence Over a Finite Field

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)503-512
Number of pages10
JournalInternational Journal of Mathematics and Mathematical Sciences
Volume4
Issue number3
DOIs
StatePublished - Jan 1 1981

Fingerprint

Permutation Matrix
Galois field
Equivalence
Equivalence class
Subgroup
Denote
Ring

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Cite this

@article{c2cbeca647be4b4da4833631cdbc225a,
title = "Permutation Matrices and Matrix Equivalence Over a Finite Field",
abstract = "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.",
author = "Mullen, {Gary Lee}",
year = "1981",
month = "1",
day = "1",
doi = "10.1155/S0161171281000367",
language = "English (US)",
volume = "4",
pages = "503--512",
journal = "International Journal of Mathematics and Mathematical Sciences",
issn = "0161-1712",
publisher = "Hindawi Publishing Corporation",
number = "3",

}

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

In: International Journal of Mathematics and Mathematical Sciences, Vol. 4, No. 3, 01.01.1981, p. 503-512.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Permutation Matrices and Matrix Equivalence Over a Finite Field

AU - Mullen, Gary Lee

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

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 -