Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Conversion of the permanent into the determinant

Author: P. M. Gibson
Journal: Proc. Amer. Math. Soc. 27 (1971), 471-476
MSC: Primary 15.20
MathSciNet review: 0279110
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Abstract: Let $ A$ be an $ n$-square $ (0,1)$-matrix with positive permanent. It is shown that if the permanent of $ A$ can be converted into a determinant by affixing $ \pm $ signs to the elements of $ A$ then $ A$ has at most $ ({n^2} + 3n - 2)/2$ positive entries. Corollaries of this result are given.

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Keywords: Permanents, determinants, $ (0,1)$-matrices, matrices over a field
Article copyright: © Copyright 1971 American Mathematical Society