| dc.contributor.author | Hamidoune, Yahya Ould |
| dc.contributor.author | Rué Perna, Juan José |
| dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
| dc.date.accessioned | 2017-05-15T09:11:57Z |
| dc.date.available | 2017-12-01T01:30:22Z |
| dc.date.issued | 2011-03-01 |
| dc.identifier.citation | Hamidoune, Y.O., Rue, J. A lower bound for the size of a Minkowski sum of dilates. "Combinatorics probability and computing", 1 Març 2011, vol. 20, núm. 2, p. 249-256. |
| dc.identifier.issn | 0963-5483 |
| dc.identifier.uri | http://hdl.handle.net/2117/104404 |
| dc.description.abstract | 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. |
| dc.format.extent | 8 p. |
| dc.language.iso | eng |
| dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
| dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
| dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Anàlisi funcional |
| dc.subject.lcsh | Functional analysis |
| dc.subject.other | Minkowski sum |
| dc.title | A lower bound for the size of a Minkowski sum of dilates |
| dc.type | Article |
| dc.subject.lemac | Anàlisi funcional |
| dc.contributor.group | Universitat Politècnica de Catalunya. MD - Matemàtica Discreta |
| dc.identifier.doi | 10.1017/S0963548310000520 |
| dc.rights.access | Open Access |
| local.identifier.drac | 17744334 |
| dc.description.version | Postprint (author's final draft) |
| local.citation.author | Hamidoune, Y.O.; Rue, J. |
| local.citation.publicationName | Combinatorics probability and computing |
| local.citation.volume | 20 |
| local.citation.number | 2 |
| local.citation.startingPage | 249 |
| local.citation.endingPage | 256 |
