A step beyond Freiman’s theorem for set addition modulo a prime"

Freiman’s 2.4-Theorem states that any set A ⊂ Z p 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...

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Detalhes bibliográficos
Autores: Candela, P., Serra, O., Spiegel, C.
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Recursos:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2072/530645
Acesso em linha:http://hdl.handle.net/2072/530645
Access Level:acceso abierto
Palavra-chave:Matemàtiques
51
Descrição
Resumo:Freiman’s 2.4-Theorem states that any set A ⊂ Z p 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/10 215 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/10 10 .