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This leads to asymptotically independent Poisson variables for numbers of various large parts. In many cases this leads to asymptotic formulas for the probability of being gap-free and for the expected values of the largest part sizes, number of distinct parts and number of parts of multiplicity<jats:italic>k<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0963548314000315","type":"journal-article","created":{"date-parts":[[2014,7,9]],"date-time":"2014-07-09T13:37:28Z","timestamp":1404913048000},"page":"686-716","source":"Crossref","is-referenced-by-count":2,"title":["Part Sizes of Smooth Supercritical Compositional Structures"],"prefix":"10.1017","volume":"23","author":[{"given":"EDWARD A.","family":"BENDER","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ZHICHENG","family":"GAO","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,7,9]]},"reference":[{"key":"S0963548314000315_ref23","volume-title":"Asymptotics and Special Functions","author":"Olver","year":"1974"},{"key":"S0963548314000315_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(74)90107-1"},{"key":"S0963548314000315_ref16","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1999.3006"},{"key":"S0963548314000315_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2005.02.008"},{"key":"S0963548314000315_ref21","first-page":"127","article-title":"Matrix compositions: A probabilistic analysis.","volume":"19","author":"Louchard","year":"2008","journal-title":"Pure Math. 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