{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:22:02Z","timestamp":1759335722162,"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 investigate the asymptotic number of elements of size $n$ in a particular class of closed lambda-terms (so-called $BCI(p)$-terms) which are related to axiom systems of combinatory logic. By deriving a differential equation for the generating function of the counting sequence we obtain a recurrence relation which can be solved asymptotically. We derive differential equations for the generating functions of the counting sequences of other more general classes of terms as well: the class of $BCK(p)$-terms and that of closed lambda-terms. Using elementary arguments we obtain upper and lower estimates for the number of closed lambda-terms of size $n$. Moreover, a recurrence relation is derived which allows an efficient computation of the counting sequence. $BCK(p)$-terms are discussed briefly.<\/jats:p>","DOI":"10.37236\/3051","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:11:38Z","timestamp":1578705098000},"source":"Crossref","is-referenced-by-count":8,"title":["Enumeration of Generalized $BCI$ Lambda-terms"],"prefix":"10.37236","volume":"20","author":[{"given":"Olivier","family":"Bodini","sequence":"first","affiliation":[]},{"given":"Dani\u00e8le","family":"Gardy","sequence":"additional","affiliation":[]},{"given":"Bernhard","family":"Gittenberger","sequence":"additional","affiliation":[]},{"given":"Alice","family":"Jacquot","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,12,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p30\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:10:34Z","timestamp":1579259434000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i4p30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,17]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/3051","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,12,17]]},"article-number":"P30"}}