{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T15:31:15Z","timestamp":1775835075217,"version":"3.50.1"},"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>Let $\\rho _n$ be the fraction of structures of \"size\" $n$ which are \"connected\"; e.g., (a) the fraction of labeled or unlabeled $n$-vertex graphs having one component, (b) the fraction of partitions of $n$ or of an $n$-set having a single part or block, or (c) the fraction of $n$-vertex forests that contain only one tree. Various authors have considered $\\lim \\rho _n$, provided it exists. It is convenient to distinguish three cases depending on the nature of the power series for the structures: purely formal, convergent on the circle of convergence, and other. We determine all possible values for the pair $(\\liminf \\rho _{n},\\;\\limsup \\rho _{n})$ in these cases. Only in the convergent case can one have $0 &lt; \\lim \\rho _{n} &lt; 1$. We study the existence of $\\lim \\rho _{n}$ in this case.<\/jats:p>","DOI":"10.37236\/1511","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:04:26Z","timestamp":1578708266000},"source":"Crossref","is-referenced-by-count":9,"title":["Asymptotics for the Probability of Connectedness and the Distribution of Number of Components"],"prefix":"10.37236","volume":"7","author":[{"given":"Jason P.","family":"Bell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Edward A.","family":"Bender","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter J.","family":"Cameron","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L. Bruce","family":"Richmond","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2000,5,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:22:55Z","timestamp":1579324975000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,5,30]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1511","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,5,30]]},"article-number":"R33"}}