A step beyond Freiman’s theorem for set addition modulo a prime
Freiman’s 2.4-Theorem states that any set (Formula Presented) 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| ≤...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universidad Autónoma de Madrid |
| Repositorio: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.uam.es:10486/708899 |
| Acceso en línea: | http://hdl.handle.net/10486/708899 https://dx.doi.org/10.5802/jtnb.1122 |
| Access Level: | acceso abierto |
| Palabra clave: | Additive Combinatorics Inverse Result Small Doubling Sumset Matemáticas |
| Sumario: | Freiman’s 2.4-Theorem states that any set (Formula Presented) 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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