{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:54Z","timestamp":1753893834979,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>For $\\lambda \\in \\mathbb{Z}$, let $\\lambda \\cdot A = \\{ \\lambda a : a \\in A\\}$. Suppose $r, h\\in \\mathbb{Z}$ are sufficiently large and comparable to each other. We prove that if $|A+A| \\le K |A|$ and $\\lambda_1, \\ldots, \\lambda_h \\le 2^r$, then \\[ |\\lambda_1 \\cdot A + \\ldots + \\lambda_h \\cdot A | \\le K^{ 7 rh \/\\ln (r+h) } |A|. \\]This improves upon a result of Bukh who shows that\\[ |\\lambda_1 \\cdot A + \\ldots + \\lambda_h \\cdot A | \\le K^{O(rh)} |A|. \\]Our main technique is to combine Bukh's idea of considering the binary expansion of $\\lambda_i$ with a result on biclique decompositions of bipartite graphs.<\/jats:p>","DOI":"10.37236\/6576","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T10:49:47Z","timestamp":1578653387000},"source":"Crossref","is-referenced-by-count":0,"title":["New Upper Bound for Sums of Dilates"],"prefix":"10.37236","volume":"24","author":[{"given":"Albert","family":"Bush","sequence":"first","affiliation":[]},{"given":"Yi","family":"Zhao","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,8,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p37\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i3p37\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,16]],"date-time":"2020-01-16T23:49:51Z","timestamp":1579218591000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i3p37"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,25]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,7,14]]}},"URL":"https:\/\/doi.org\/10.37236\/6576","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,8,25]]},"article-number":"P3.37"}}