{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:05:48Z","timestamp":1761609948806,"version":"3.41.2"},"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>Let $X$ be a finite collection of sets. We count the number of ways a disjoint union of $n-1$ subsets in $X$ is a set in $X$, and estimate the number from above by $|X|^{c(n)}$ where $$c(n)=\\left(1-\\frac{(n-1)\\ln (n-1)}{n\\ln n} \\right)^{-1}.$$ This extends the recent result of Kane-Tao, corresponding to the case $n=3$ where $c(3)\\approx 1.725$, to an arbitrary finite number of disjoint $n-1$ partitions.\u00a0<\/jats:p>","DOI":"10.37236\/7042","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:53:48Z","timestamp":1578671628000},"source":"Crossref","is-referenced-by-count":1,"title":["Convolution Estimates and Number of Disjoint Partitions"],"prefix":"10.37236","volume":"24","author":[{"given":"Paata","family":"Ivanisvili","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,6,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p43\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i2p43\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:55:44Z","timestamp":1579236944000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i2p43"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,30]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,4,13]]}},"URL":"https:\/\/doi.org\/10.37236\/7042","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,6,30]]},"article-number":"P2.43"}}