A lower bound for the size of a Minkowski sum of dilates
Let A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of several dilates was obtained by Bukh. The unique known exact bound concerns the sum |A + k·A|, where k is a prime and |A| is large. In its full generality, this bound is due to Cilleruelo, Serra and the fir...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/104404 |
| Acesso em linha: | https://hdl.handle.net/2117/104404 https://dx.doi.org/10.1017/S0963548310000520 |
| Access Level: | acceso abierto |
| Palavra-chave: | Functional analysis Minkowski sum Anàlisi funcional Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Anàlisi funcional |
| Resumo: | Let A be a finite non-empty set of integers. An asymptotic estimate of the size of the sum of several dilates was obtained by Bukh. The unique known exact bound concerns the sum |A + k·A|, where k is a prime and |A| is large. In its full generality, this bound is due to Cilleruelo, Serra and the first author. Let k be an odd prime and assume that |A| > 8kk. A corollary to our main result states that |2·A + k·A|=(k+2)|A|-k2-k+2. Notice that |2·P+k·P|=(k+2)|P|-2k, if P is an arithmetic progression. |
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