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dc.contributor.authorHamidoune, Yahya Ould
dc.contributor.authorLópez Masip, Susana-Clara
dc.contributor.authorPlagne, Alain
dc.date.accessioned2019-06-14T12:08:31Z
dc.date.available2019-06-14T12:08:31Z
dc.date.issued2013
dc.identifier.issn0195-6698
dc.identifier.urihttp://hdl.handle.net/10459.1/66455
dc.description.abstractLet A, B and S be subsets of a finite Abelian group G. The restricted sumset of A and B with respect to S is defined as A ∧S B = {a + b : a ∈ A, b ∈ B and a − b /∈ S}. Let LS = maxz∈G |{(x, y) : x, y ∈ G, x + y = z and x − y ∈ S}|. A simple application of the pigeonhole principle shows that |A| + |B| > |G| + LS implies A ∧S B = G. We then prove that if |A| + |B| = |G| + LS then |A ∧S B| ≥ |G| − 2|S|. We also characterize the triples of sets (A, B, S) such that |A| + |B| = |G| + LS and |A ∧S B| = |G| − 2|S|. Moreover, in this case, we also provide the structure of the set G \ (A ∧S B).
dc.description.sponsorshipThis research was done when the second author was visiting Université Pierre et Marie Curie, E. Combinatoire, Paris, supported by the Ministry of Education, Spain, under the National Mobility Programme of Human Resources, Spanish National Programme I-D-I 2008–2011.
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherElsevier
dc.relation.isformatofVersió postprint del document publicat a: https://doi.org/10.1016/j.ejc.2013.05.020
dc.relation.ispartofEuropean Journal of Combinatorics, 2013, vol. 34, num. 8, p. 1348-1364
dc.rightscc-by-nc-nd (c) Elsevier, 2013
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleLarge restricted sumsets in general Abelian groups
dc.typeinfo:eu-repo/semantics/article
dc.date.updated2019-06-14T12:08:31Z
dc.identifier.idgrec028489
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.identifier.doihttps://doi.org/10.1016/j.ejc.2013.05.020


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cc-by-nc-nd (c) Elsevier, 2013
Except where otherwise noted, this item's license is described as cc-by-nc-nd (c) Elsevier, 2013