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arXiv · 2109.00618

Rank of matrices with entries from a multiplicative group

Noga Alon·Jozsef Solymosi
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Abstract

We establish lower bounds on the rank of matrices in which all but the diagonal entries lie in a multiplicative group of small rank. Applying these bounds we show that the distance sets of finite pointsets in $\mathbb{R}^d$ generate high rank multiplicative groups and that multiplicative groups of small rank cannot contain large sumsets.

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Noga Alon, Jozsef Solymosi. 2021-09-01. Rank of matrices with entries from a multiplicative group. https://arxiv.org/abs/2109.00618

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