{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:56Z","timestamp":1753893836183,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We define the notion of asymptotically free for locally restricted\u00a0compositions, which means roughly that large parts can often be\u00a0replaced by any larger parts.\u00a0Two well-known examples are Carlitz and alternating compositions.\u00a0We show that large parts have asymptotically geometric distributions.\u00a0This leads to asymptotically independent Poisson variables for numbers of\u00a0various large parts.\u00a0Based on this we obtain asymptotic formulas for the probability of\u00a0being gap free and for the expected values of the largest\u00a0part, number of distinct parts and number of parts of multiplicity $k$,\u00a0all accurate to $o(1)$.<\/jats:p>","DOI":"10.37236\/2571","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:12:04Z","timestamp":1578712324000},"source":"Crossref","is-referenced-by-count":2,"title":["Locally Restricted Compositions IV. Nearly Free Large Parts and Gap-Freeness"],"prefix":"10.37236","volume":"19","author":[{"given":"Edward A.","family":"Bender","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E. Rodney","family":"Canfield","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhicheng","family":"Gao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2012,10,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p14\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v19i4p14\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:28:30Z","timestamp":1579300110000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v19i4p14"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,25]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2012,10,18]]}},"URL":"https:\/\/doi.org\/10.37236\/2571","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2012,10,25]]},"article-number":"P14"}}