Rank of Matrices with Entries from a Multiplicative Group

Noga Alon; József Solymosi

doi:10.1093/imrn/rnac183

Rank of Matrices with Entries from a Multiplicative Group

Noga Alon, József Solymosi

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 generate high-rank multiplicative groups and that multiplicative groups of small rank cannot contain large sumsets.

Original language	English (US)
Pages (from-to)	12383-12399
Number of pages	17
Journal	International Mathematics Research Notices
Volume	2023
Issue number	14
DOIs	https://doi.org/10.1093/imrn/rnac183
State	Published - Jul 1 2023

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnac183

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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 generate high-rank multiplicative groups and that multiplicative groups of small rank cannot contain large sumsets.",

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AB - 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 generate high-rank multiplicative groups and that multiplicative groups of small rank cannot contain large sumsets.

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Rank of Matrices with Entries from a Multiplicative Group

Abstract

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