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. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/36929 |
| Date | January 1966 |
| Creators | Horn, Peter J. |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| 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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