A step beyond Freiman’s theorem for set addition modulo a prime
Freiman’s 2.4-Theorem states that any set A¿Zp satisfying |2A|=2.4|A|-3 and |A|<p/35 can be covered by an arithmetic progression of length at most |2A|-|A|+1. A more general result of Green and Ruzsa implies that this covering property holds for any set satisfying |2A|=3|A|-4 as long as the rathe...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/343738 |
| Acceso en línea: | https://hdl.handle.net/2117/343738 https://dx.doi.org/10.5802/jtnb.1122 |
| Access Level: | acceso abierto |
| Palabra clave: | Classificació AMS::11 Number theory Classificació AMS::05 Combinatorics::05B Designs and configurations Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | Freiman’s 2.4-Theorem states that any set A¿Zp satisfying |2A|=2.4|A|-3 and |A|<p/35 can be covered by an arithmetic progression of length at most |2A|-|A|+1. A more general result of Green and Ruzsa implies that this covering property holds for any set satisfying |2A|=3|A|-4 as long as the rather strong density requirement |A|<p/10215 is satisfied. We present a version of this statement that allows for sets satisfying |2A|=2.48|A|-7 with the more modest density requirement of |A|<p/1010. |
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