{"paper":{"title":"Bounds on the cardinality of restricted sumsets in $\\mathbb{Z}_{p}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bernardo Llano, Gabriel Bengochea","submitted_at":"2018-03-26T03:39:44Z","abstract_excerpt":"In this paper we present a procedure which allows to transform a subset $A$ of $\\mathbb{Z}_{p}$ into a set $ A'$ such that $ |2\\hspace{0.15cm}\\widehat{} A'|\\leq|2\\hspace{0.15cm}\\widehat{} A | $, where $2\\hspace{0.15cm}\\widehat{} A$ is defined to be the set $\\left\\{a+b:a\\neq b,\\;a,b\\in A\\right\\}$. From this result, we get some lower bounds for $ |2\\hspace{0.15cm}\\widehat{} A| $. Finally, we give some remarks related to the problem for which sets $A\\subset \\mathbb{Z}_{p}$ we have the equality $|2\\hspace{0.15cm}\\widehat{} A|=2|A|-1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09400","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}