{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:09Z","timestamp":1753893849172,"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>The dartboard problem is to arrange $n$ numbers on a circle to obtain maximum risk, which is the sum of the $q$-th power of the absolute differences of adjacent numbers, for $q\\ge 1$. Curtis showed that the dartboard problem admits a greedy algorithm. We generalize the dartboard problem by considering more circles and the goal is to arrange $kn$ number on $k$ circles to obtain the maximum risk. In this paper, we characterize an optimal arrangement for $k=2$ and show that the generalized dartboard problem also admits a greedy algorithm.<\/jats:p>","DOI":"10.37236\/965","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:49:37Z","timestamp":1578700177000},"source":"Crossref","is-referenced-by-count":0,"title":["Arranging Numbers on Circles to Reach Maximum Total Variations"],"prefix":"10.37236","volume":"14","author":[{"given":"Ying-Jie","family":"Liao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min-Zheng","family":"Shieh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shi-Chun","family":"Tsai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2007,6,28]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r47\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r47\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:02:22Z","timestamp":1579302142000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,6,28]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/965","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,6,28]]},"article-number":"R47"}}