{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T14:13:16Z","timestamp":1770473596722,"version":"3.49.0"},"reference-count":0,"publisher":"University of Calgary","issue":"1","license":[{"start":{"date-parts":[[2025,4,30]],"date-time":"2025-04-30T00:00:00Z","timestamp":1745971200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nd\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Contrib Discrete Math"],"abstract":"<jats:p>Let $A$ be a set of $k$ integers such that $A\\subseteq [0, l]$, $0, l\\in A$ and $\\gcd(A)=1$. Let $2^{\\wedge}A$ denote the set of all sums of two distinct elements of $A$. Write $W=\\{w\\in [0, l]\\backslash A: w,w+l\\not\\in 2^{\\wedge}A\\}$. In this paper, we obtain the upper bound of $|W|$ with some restrictions on $l$. As an application, we show that the Freiman-Lev conjecture is true for $l=2k-4$ using the structure of $A$ with $|W|=2$.<\/jats:p>","DOI":"10.55016\/ojs\/cdm.v20i1.75917","type":"journal-article","created":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T16:46:48Z","timestamp":1762620408000},"page":"42-59","source":"Crossref","is-referenced-by-count":1,"title":["On Freiman-Lev conjecture"],"prefix":"10.55016","volume":"20","author":[{"given":"Yujie","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min","family":"Tang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"13844","published-online":{"date-parts":[[2025,4,30]]},"container-title":["Contributions to Discrete Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/cdm.ucalgary.ca\/article\/download\/75917\/58188","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/cdm.ucalgary.ca\/article\/download\/75917\/58188","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T22:21:05Z","timestamp":1764109265000},"score":1,"resource":{"primary":{"URL":"https:\/\/cdm.ucalgary.ca\/article\/view\/75917"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2025,4,30]]}},"URL":"https:\/\/doi.org\/10.55016\/ojs\/cdm.v20i1.75917","relation":{},"ISSN":["1715-0868"],"issn-type":[{"value":"1715-0868","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,30]]}}}