{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T20:10:16Z","timestamp":1772827816338,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>The weighted binomial sum $f_m(r)=2^{-r}\\sum_{i=0}^r\\binom{m}{i}$ arises in coding theory and information theory. We prove that, for $m\\not\\in\\{0,3,6,9,12\\}$, the maximum value of $f_m(r)$ with $0\\le r\\le m$ occurs when $r=\\lfloor m\/3\\rfloor+1$. We also show this maximum value is asymptotic to $\\frac{3}{\\sqrt{{\\pi}m}}\\left(\\frac{3}{2}\\right)^m$ as $m\\to\\infty$.\u00a0<\/jats:p>","DOI":"10.37236\/10751","type":"journal-article","created":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T08:40:20Z","timestamp":1649407220000},"source":"Crossref","is-referenced-by-count":3,"title":["On the Maximum of the Weighted Binomial Sum $2^{-r}\\sum_{i=0}^r\\binom{m}{i}$"],"prefix":"10.37236","volume":"29","author":[{"given":"Stephen","family":"Glasby","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gerhard","family":"Paseman","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2022,4,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p5\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v29i2p5\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T08:40:20Z","timestamp":1649407220000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v29i2p5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,1]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2022,4,8]]}},"URL":"https:\/\/doi.org\/10.37236\/10751","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,1]]},"article-number":"P2.5"}}