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Finite Field Models in Arithmetic Combinatorics – Twenty Years On

Published online by Cambridge University Press:  23 May 2024

By
Sarah Peluse
Edited by
Felix Fischer  and
Robert Johnson
Felix Fischer
Affiliation:
Queen Mary University of London
Robert Johnson
Affiliation:
Queen Mary University of London
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Summary

About twenty years ago, Green wrote a survey article on the utility of looking at toy versions over finite fields of problems in additive combinatorics. This survey was extremely influential, and the rapid development of additive combinatorics necessitated a follow-up article ten years later, which was written by Wolf. Since the publication of Wolf’s article, an immense amount of progress has been made on several central open problems in additive combinatorics in both the finite field model and integer settings. This survey covers some of the most significant results of the past ten years and suggests future directions.

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Surveys in Combinatorics 2024 , pp. 159 - 200
Publisher: Cambridge University Press
Print publication year: 2024

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