{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:37:28Z","timestamp":1787323048023,"version":"build-2736575974"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2023,3,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Let [Formula: see text] be a commutative group and [Formula: see text] and [Formula: see text] be nonempty finite subsets of [Formula: see text] and [Formula: see text]. Kneser\u2019s theorem is a fundamental result in additive number theory, and it establishes that [Formula: see text]. For any subset [Formula: see text] of [Formula: see text], write [Formula: see text]. For any [Formula: see text], set [Formula: see text]. An important problem in additive number theory is to find a Kneser-type theorem for the restricted sumsets [Formula: see text]. In particular, more than 20 years ago V. Lev proved that if [Formula: see text] [Formula: see text], for all [Formula: see text] (resp., [Formula: see text]) there is at most one [Formula: see text] (resp., [Formula: see text]) such that [Formula: see text] (resp., [Formula: see text]), and [Formula: see text]; then [Formula: see text]. In the same paper, Lev proposed as a problem to improve [Formula: see text] to something of the form [Formula: see text] with [Formula: see text] whenever [Formula: see text]. Lev\u2019s problem has been solved for some particular groups and some specific subsets [Formula: see text] of [Formula: see text]. However, it remains open for arbitrary groups and arbitrary large subsets [Formula: see text] of [Formula: see text]. Here, as a consequence of the main result of this paper, it is shown that if we take [Formula: see text] instead of [Formula: see text] in the lower bound of [Formula: see text], then indeed we can take as the coefficient of [Formula: see text] something of the form [Formula: see text] with [Formula: see text] whenever [Formula: see text].<\/jats:p>","DOI":"10.1137\/22m1476150","type":"journal-article","created":{"date-parts":[[2023,1,18]],"date-time":"2023-01-18T13:50:05Z","timestamp":1674049805000},"page":"83-93","source":"Crossref","is-referenced-by-count":0,"title":["A Kneser-Type Theorem for Restricted Sumsets"],"prefix":"10.1137","volume":"37","author":[{"given":"Mario","family":"Huicochea","sequence":"first","affiliation":[{"name":"CONACYT\/UAZ, Zacatecas, Mexico."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,1,20]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-015-0546-1"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-00416-7"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2009.06.028"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2008.05.009"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejc.2013.05.020"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610700008863"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.37236\/1482"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1023\/A:1015248607819"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.5802\/jtnb.485"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.4064\/aa171-3-2"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3845-2"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02773597"},{"key":"ref13","first-page":"73","volume":"7","author":"Petrov F.","year":"2017","journal-title":"Mosc. 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