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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


An upper bound for the permanent of a fully indecomposable matrix

Author: Thomas H. Foregger
Journal: Proc. Amer. Math. Soc. 49 (1975), 319-324
MSC: Primary 15A15
MathSciNet review: 0369385
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Abstract: Let $ A$ be an $ n \times n$ fully indecompasable matrix with nonnegative integer entries and let $ \sigma (A)$ denote the sum of the entries of $ A$. We prove that $ {\text{per}}(A) \leq {2^{\sigma (A) - 2n}} + 1$ and give necessary and sufficient conditions for equality to hold.

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PII: S 0002-9939(1975)0369385-4
Keywords: Permanent, fully indecomposable, $ (0,1)$ matrix
Article copyright: © Copyright 1975 American Mathematical Society