UBC Theses and Dissertations

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UBC Theses and Dissertations

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.

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