A remark on an equivalence of two versions of Polya's permanent problem

Ratsiri Sanguanwong; Kiji Rodtes

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arXiv · 2012.01278

A remark on an equivalence of two versions of Polya's permanent problem

Ratsiri Sanguanwong·Kiji Rodtes

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Abstract

In 2004, some equivalent versions of Polya's permanent problem were listed in 24 versions. However, there is a flaw on the theorem that affirms an equivalence of version 11 and 12. In order to correct the slip, we provide a characterization when the determinant and permanent of a given nonnegative matrix are equal. Moreover, the new characterization yields necessary and sufficient conditions for the equality of the determinant and permanent of powers of a given nonnegative matrix.

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Ratsiri Sanguanwong, Kiji Rodtes. 2020-12-02. A remark on an equivalence of two versions of Polya's permanent problem. https://arxiv.org/abs/2012.01278

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