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The permanent of a certain matrix Horn, Peter J.
Abstract
The purpose of this thesis is to attempt to evaluate the permanent function of a n×n complex matrix with entries aij = θij being a primitive n root of unity. If this matrix is denoted by An then its permanent function is given by per An = [formula omitted] In this thesis the following results are proved. Per An is always an integer; with per An ≡ 0 mod n. If n is even per An = 0. For n odd however, the problem is in general not resolved. It is shown that if n=p² with p a prime, that per An = 0 mod p⁴ and that for any prime n, per An can be narrowed down to be one of a restricted class of numbers.
Item Metadata
| Title |
The permanent of a certain matrix
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
1966
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| Description |
The purpose of this thesis is to attempt to evaluate the permanent function of a n×n complex matrix with entries aij = θij being a primitive n root of unity.
If this matrix is denoted by An then its permanent function is given by
per An = [formula omitted]
In this thesis the following results are proved.
Per An is always an integer; with per An ≡ 0 mod n.
If n is even per An = 0.
For n odd however, the problem is in general not resolved.
It is shown that if n=p² with p a prime, that per An = 0 mod p⁴ and that for any prime n, per An can be narrowed down to be one of a restricted class of numbers.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2011-08-26
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| Provider |
Vancouver : University of British Columbia Library
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| Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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| DOI |
10.14288/1.0080613
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| URI | |
| Degree | |
| Program | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.