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arXiv · 1608.02844

An update on a few permanent conjectures

Fuzhen Zhang
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Abstract

We review and update on a few conjectures concerning matrix permanent that are easily stated, understood, and accessible to general math audience. They are: Soules permanent-on-top conjecture${}^\dagger$, Lieb permanent dominance conjecture, Bapat and Sunder conjecture${}^\dagger$ on Hadamard product and diagonal entries, Chollet conjecture on Hadamard product, Marcus conjecture on permanent of permanents, and several other conjectures. Some of these conjectures are recently settled; some are still open. We also raise a few new questions for future study. (${}^\dagger$conjectures have been recently settled negatively.)

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Fuzhen Zhang. 2016-08-09. An update on a few permanent conjectures. https://arxiv.org/abs/1608.02844

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