{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:59Z","timestamp":1753893779770,"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>A tournament sequence is an increasing sequence of positive integers $(t_1,t_2,\\ldots)$ such that $t_1=1$ and $t_{i+1} \\leq 2t_i$. A Meeussen sequence is an increasing sequence of positive integers $(m_1,m_2,\\ldots)$ such that $m_1=1$, every nonnegative integer is the sum of a subset of the $\\{m_i\\}$, and each integer $m_i-1$ is the sum of a unique such subset. We show that these two properties are isomorphic.  That is, we present a bijection between tournament and Meeussen sequences which respects the natural tree structure on each set.  We also present an efficient technique for counting the number of tournament sequences of length $n$, and discuss the asymptotic growth of this number.  The counting technique we introduce is suitable for application to other well-behaved counting problems of the same sort where a closed form or generating function cannot be found.<\/jats:p>","DOI":"10.37236\/1522","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:02:51Z","timestamp":1578708171000},"source":"Crossref","is-referenced-by-count":1,"title":["Tournament Sequences and Meeussen Sequences"],"prefix":"10.37236","volume":"7","author":[{"given":"Matthew","family":"Cook","sequence":"first","affiliation":[]},{"given":"Michael","family":"Kleber","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,9,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r44\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r44\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:21:59Z","timestamp":1579324919000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1522","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,9,5]]},"article-number":"R44"}}