{"paper":{"title":"On the minimum size of restricted sumsets in cyclic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"B\\'ela Bajnok","submitted_at":"2013-05-09T16:42:30Z","abstract_excerpt":"For positive integers $n$, $m$, and $h$, we let $\\rho \\hat{\\;}(\\mathbb{Z}_n, m, h)$ denote the minimum size of the $h$-fold restricted sumset among all $m$-subsets of the cyclic group of order $n$. The value of $\\rho \\hat{\\;}(\\mathbb{Z}_n, m, h)$ was conjectured for prime values of $n$ and $h=2$ by Erd\\H{o}s and Heilbronn in the 1960s; Dias da Silva and Hamidoune proved the conjecture in 1994 and generalized it for an arbitrary $h$, but little is known about the case when $n$ is composite. Here we exhibit an explicit upper bound for all $n$, $m$, and $h$; our bound is tight for all known cases"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2141","kind":"arxiv","version":2},"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"}