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On growth in an abstract plane

Gill, Nick; Helfgott, Harald A. and Rudnev, Misha (2015). On growth in an abstract plane. Proceedings of the American Mathematical Society, 143(8) pp. 3593–3602.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1090/proc/12309
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Abstract

There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over $\mathbb{R}$ or $\mathbb{C}$, geometric statements on growth often have geometric proofs, what little is known over finite fields rests on arithmetic proofs.

We discuss strategies for geometric proofs of growth over finite fields, and show that growth can be defined and proven in an abstract projective plane -- even one with weak axioms.

Item Type: Journal Item
Copyright Holders: 2015 American Mathematical Society
ISSN: 1088-6826
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
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Item ID: 38079
Depositing User: Nick Gill
Date Deposited: 31 Jul 2013 12:35
Last Modified: 07 Dec 2018 12:30
URI: http://oro.open.ac.uk/id/eprint/38079
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