{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:55Z","timestamp":1753893835926,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider the problem of reconstructing a set of real numbers up to  translation from the multiset of its subsets of fixed size, given up  to translation. This is impossible in general: for instance almost all  subsets of $\\mathbb{Z}$ contain infinitely many translates of every finite subset  of $\\mathbb{Z}$. We therefore restrict our attention to subsets of $\\mathbb{R}$ which are  locally finite; those which contain only finitely many translates  of any given finite set of size at least 2. We prove that every locally finite subset of $\\mathbb{R}$ is reconstructible from  the multiset of its 3-subsets, given up to translation.<\/jats:p>","DOI":"10.37236\/1452","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:00:50Z","timestamp":1578708050000},"source":"Crossref","is-referenced-by-count":4,"title":["Reconstructing Subsets of Reals"],"prefix":"10.37236","volume":"6","author":[{"given":"A. J.","family":"Radcliffe","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. D.","family":"Scott","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[1999,3,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r20\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r20\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:33:17Z","timestamp":1579325597000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,3,15]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1452","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1999,3,15]]},"article-number":"R20"}}