{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T14:47:47Z","timestamp":1648738067923},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2019,6]]},"abstract":"<jats:p> We consider the problem of computing [Formula: see text], the number of unlabeled graded lattices of rank [Formula: see text] that contain [Formula: see text] coatoms and [Formula: see text] atoms. More specifically, we do this when [Formula: see text] is fairly small, but [Formula: see text] may be large. For this task, we describe a computational method that combines constructive listing of basic cases and tools from enumerative combinatorics. With this method, we compute the exact values of [Formula: see text] for [Formula: see text] and [Formula: see text]. <\/jats:p><jats:p> We also show that, for any fixed [Formula: see text], there exists a quasipolynomial in [Formula: see text] that matches with [Formula: see text] for all [Formula: see text] above a small value. We explicitly determine these quasipolynomials for [Formula: see text], thus finding closed form expressions of [Formula: see text] for [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196719500206","type":"journal-article","created":{"date-parts":[[2019,1,11]],"date-time":"2019-01-11T06:27:52Z","timestamp":1547188072000},"page":"663-680","source":"Crossref","is-referenced-by-count":0,"title":["Counting graded lattices of rank 3 that have few coatoms"],"prefix":"10.1142","volume":"29","author":[{"given":"Jukka","family":"Kohonen","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Helsinki, PO Box 68, FI-00014 Helsinki, Finland"}]}],"member":"219","published-online":{"date-parts":[[2019,6,18]]},"reference":[{"key":"S0218196719500206BIB001","doi-asserted-by":"publisher","DOI":"10.1201\/9781439895153"},{"key":"S0218196719500206BIB002","volume-title":"An Introduction to Number Theoretic Combinatorics","author":"Beekman R. M.","year":"2017"},{"key":"S0218196719500206BIB003","doi-asserted-by":"publisher","DOI":"10.1017\/9781108277457"},{"key":"S0218196719500206BIB006","volume":"9","author":"Ern\u00e9 M.","year":"2002","journal-title":"Electron. J. Comb."},{"key":"S0218196719500206BIB008","volume-title":"Graphical Enumeration","author":"Harary F.","year":"1973"},{"key":"S0218196719500206BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/PL00013837"},{"key":"S0218196719500206BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00012-015-0348-x"},{"key":"S0218196719500206BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-5060(08)70708-8"},{"key":"S0218196719500206BIB012","first-page":"58","volume":"247","author":"Klotz W.","year":"1971","journal-title":"J. Reine Angew. Math."},{"key":"S0218196719500206BIB014","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1979-0514837-9"},{"key":"S0218196719500206BIB018","volume-title":"Enumerative Combinatorics","volume":"1","author":"Stanley R. P.","year":"2012","edition":"2"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196719500206","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:29:06Z","timestamp":1565098146000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196719500206"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6]]},"references-count":11,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2019,6,18]]},"published-print":{"date-parts":[[2019,6]]}},"alternative-id":["10.1142\/S0218196719500206"],"URL":"https:\/\/doi.org\/10.1142\/s0218196719500206","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,6]]}}}