{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:06Z","timestamp":1753893786324,"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>An investigation of the size of $S+S$ for a finite Beatty sequence $S=(s_i)=(\\lfloor i\\alpha+\\gamma \\rfloor)$, where $\\lfloor \\hphantom{x} \\rfloor$ denotes \"floor\", $\\alpha$, $\\gamma$ are real with $\\alpha\\ge 1$, and $0\\le i \\le k-1$ and $k\\ge 3$. For $\\alpha&gt;2$, it is shown that $|S+S|$ depends on the number of \"centres\" of the Sturmian word $\\Delta S=(s_i-s_{i-1})$, and hence that $3(k-1)\\le |S+S|\\le 4k-6$ if $S$ is not an arithmetic progression. A formula is obtained for the number of centres of certain finite periodic Sturmian words, and this leads to further information about $|S+S|$ in terms of finite nearest integer continued fractions.<\/jats:p>","DOI":"10.37236\/1614","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:15:46Z","timestamp":1578708946000},"source":"Crossref","is-referenced-by-count":3,"title":["Sumsets of Finite Beatty Sequences"],"prefix":"10.37236","volume":"8","author":[{"given":"Jane","family":"Pitman","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,8,15]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i2r15\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v8i2r15\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:22:06Z","timestamp":1579324926000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v8i2r15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,8,15]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2001,2,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1614","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,8,15]]},"article-number":"R15"}}