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arXiv · 2008.04592

Dot-product sets and simplices over finite rings

Nguyen Van The·Le Anh Vinh
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Abstract

In this paper, we study dot-product sets and $k$-simplices in vector spaces over finite rings. We show that if $E$ is sufficiently large then the dot-product set of $E$ covers the whole ring. In higher dimensional cases, if $E$ is sufficiently large then the set of simplices and the set of dot-product simplices determined by $E$, up to congurence, have positive densities.

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Nguyen Van The, Le Anh Vinh. 2020-08-11. Dot-product sets and simplices over finite rings. https://arxiv.org/abs/2008.04592

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