{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T04:27:42Z","timestamp":1666067262467},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2018,5,29]],"date-time":"2018-05-29T00:00:00Z","timestamp":1527552000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Order"],"published-print":{"date-parts":[[2019,7]]},"DOI":"10.1007\/s11083-018-9459-2","type":"journal-article","created":{"date-parts":[[2018,5,29]],"date-time":"2018-05-29T06:29:48Z","timestamp":1527575388000},"page":"119-157","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Framework for the Systematic Determination of the Posets on n Points with at Least \u03c4 \u22c5 2n Downsets"],"prefix":"10.1007","volume":"36","author":[{"given":"Frank","family":"a Campo","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,5,29]]},"reference":[{"key":"9459_CR1","volume-title":"Kombinatorik I. Grundlagen und Z\u00e4hltheorie","author":"M Aigner","year":"1975","unstructured":"Aigner, M.: Kombinatorik I. Grundlagen und Z\u00e4hltheorie. Springer-Verlag, Berlin (1975)"},{"key":"9459_CR2","first-page":"1469","volume":"200","author":"P Alexandroff","year":"1935","unstructured":"Alexandroff, P.: Sur les espaces discrets. Comptes Rendus de l\u2019Acad\u00e9mie des Sciences 200, 1469\u20131471 (1935)","journal-title":"Comptes Rendus de l\u2019Acad\u00e9mie des Sciences"},{"key":"9459_CR3","first-page":"501","volume":"2","author":"P Alexandroff","year":"1937","unstructured":"Alexandroff, P.: Diskrete R\u00e4ume. Mat. Sb. (N.S.) 2, 501\u2013518 (1937)","journal-title":"Mat. Sb. (N.S.)"},{"key":"9459_CR4","unstructured":"Benoumhani, M.: The number of topologies on a finite set. J. Integer Seq. 9, Article 06.2.6 (2006)"},{"key":"9459_CR5","unstructured":"Benoumhani, M., Kolli, M.: Finite topologies and partitions. J. Integer Seq. 13, Article 10.3.5 (2010)"},{"key":"9459_CR6","unstructured":"Birkhoff, G.: Lattice Theory, 3rd edn., vol. 25. Proc. Amer. Math. Soc. Coll Publ., Providence (1973)"},{"key":"9459_CR7","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1023\/A:1016543307592","volume":"19","author":"G Brinkmann","year":"2002","unstructured":"Brinkmann, G., McKay, B. D.: Posets on up to 16 Points. Order 19, 147\u2013179 (2002)","journal-title":"Order"},{"key":"9459_CR8","unstructured":"Brinkmann, G., McKay, B. D.: Counting unlabelled topologies and transitive relations. J. Integer Seq. 8, Article 05.2.1 (2005)"},{"key":"9459_CR9","doi-asserted-by":"publisher","first-page":"276","DOI":"10.1016\/0095-8956(72)90064-0","volume":"13","author":"KK-H Butler","year":"1972","unstructured":"Butler, K. K. -H.: The number of partially ordered sets. J. Combin. Theory (B) 13, 276\u2013289 (1972)","journal-title":"J. Combin. Theory (B)"},{"key":"9459_CR10","unstructured":"Butler, K. K. -H., Markowsky, G.: Enumeration of finite topologies. In: Proc. 4th Southeastern Conf. on Combinatorics Graph Theory and Computing, pp. 169\u2013184. Winnipeg (1973)"},{"key":"9459_CR11","unstructured":"a Campo, F., Ern\u00e9, M.: Exponential functions of finite posets and the number of extensions with a fixed set of minimal points. To appear in J. Combin. Math. Combin. Comput."},{"key":"9459_CR12","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/BF00383201","volume":"7","author":"JC Culberson","year":"1991","unstructured":"Culberson, J. C., Rawlins, J. E.: New results from an algorithm for counting posets. Order 7, 361\u2013374 (1991)","journal-title":"Order"},{"key":"9459_CR13","volume-title":"Struktur- und Anzahlformeln f\u00fcr Topologien auf endlichen Mengen","author":"M Ern\u00e9","year":"1972","unstructured":"Ern\u00e9, M.: Struktur- und Anzahlformeln f\u00fcr Topologien auf endlichen Mengen. Westf\u00e4lische Wilhelms-Universit\u00e4t zu M\u00fcnster, PhD Dissertation (1972)"},{"key":"9459_CR14","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/BF01173716","volume":"11","author":"M Ern\u00e9","year":"1974","unstructured":"Ern\u00e9, M: Struktur- und Anzahlformeln f\u00fcr Topologien auf endlichen Mengen. Manuscripta Math. 11, 221\u2013259 (1974)","journal-title":"Manuscripta Math."},{"key":"9459_CR15","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/0012-365X(81)90202-8","volume":"35","author":"M Ern\u00e9","year":"1981","unstructured":"Ern\u00e9, M.: On the cardinalities of finite topologies and the number of Antichains in partially ordered sets. Discrete Math. 35, 119\u2013133 (1981)","journal-title":"Discrete Math."},{"key":"9459_CR16","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/0012-365X(92)90131-X","volume":"105","author":"M Ern\u00e9","year":"1992","unstructured":"Ern\u00e9, M.: The number of partially ordered sets with more points than incomparable pairs. Discrete Math. 105, 49\u201360 (1992)","journal-title":"Discrete Math."},{"key":"9459_CR17","doi-asserted-by":"crossref","first-page":"#R24","DOI":"10.37236\/1641","volume":"9","author":"M Ern\u00e9","year":"2002","unstructured":"Ern\u00e9, M., Heitzig, J., Reinhold, J.: On the number of distributive lattices. Electron. J. Comb. 9, #R24 (2002)","journal-title":"Electron. J. Comb."},{"key":"9459_CR18","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1007\/BF00383446","volume":"8","author":"M Ern\u00e9","year":"1991","unstructured":"Ern\u00e9, M., Stege, K.: Counting finite posets and topologies. Order 8, 247\u2013265 (1991)","journal-title":"Order"},{"key":"9459_CR19","first-page":"65","volume":"40","author":"M Ern\u00e9","year":"1995","unstructured":"Ern\u00e9, M., Stege, K.: Combinatorial applications of ordinal sum decompositions. Ars Combinatoria 40, 65\u201388 (1995)","journal-title":"Ars Combinatoria"},{"key":"9459_CR20","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1023\/A:1006431609027","volume":"17","author":"J Heitzig","year":"2000","unstructured":"Heitzig, J., Reinhold, J.: The number of unlabeled orders on fourteen elements. Order 17, 333\u2013341 (2000)","journal-title":"Order"},{"key":"9459_CR21","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1007\/PL00013837","volume":"48","author":"J Heitzig","year":"2002","unstructured":"Heitzig, J., Reinhold, J.: Counting finite lattices. Algebra Universalis 48, 43\u201353 (2002)","journal-title":"Algebra Universalis"},{"key":"9459_CR22","unstructured":"Kolli, M.: Direct and elementary approach to enumerate topologies on a finite set. J. Integer Seq. 10, Article 07.3.1 (2007)"},{"key":"9459_CR23","doi-asserted-by":"publisher","unstructured":"Kolli, M.: On the cardinality of the T 0-topologies on a finite set. Intern. J. of Combin., Article ID 798074. (2014) https:\/\/doi.org\/10.1155\/2014\/798074","DOI":"10.1155\/2014\/798074"},{"key":"9459_CR24","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/0012-365X(75)90008-4","volume":"11","author":"R Parchmann","year":"1975","unstructured":"Parchmann, R.: On the cardinalities of finite topologies. Discrete Math. 11, 161\u2013172 (1975)","journal-title":"Discrete Math."},{"key":"9459_CR25","unstructured":"Pfeiffer, G.: Counting transitive relations. J. Integer Seq., 7 (2004), Article 04.3.2"},{"key":"9459_CR26","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1016\/j.jcta.2009.05.002","volume":"117","author":"K Ragnarsson","year":"2010","unstructured":"Ragnarsson, K., Tenner, B. E.: Obtainable sizes of topologies on finite sets. J. Combin. Theory (A) 117, 138\u2013151 (2010)","journal-title":"J. Combin. Theory (A)"},{"key":"9459_CR27","doi-asserted-by":"publisher","first-page":"1344","DOI":"10.1090\/S0002-9939-1966-0217771-X","volume":"17","author":"H Sharp","year":"1966","unstructured":"Sharp, H.: Quasi-orderings and topologies on finite sets. Proc. Amer. Math. Soc. 17, 1344\u20131349 (1966)","journal-title":"Proc. Amer. Math. Soc."},{"key":"9459_CR28","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/S0021-9800(68)80031-6","volume":"5","author":"H Sharp","year":"1968","unstructured":"Sharp, H.: Cardinality of finite topologies. J. Combin. Theory 5, 82\u201386 (1968)","journal-title":"J. Combin. Theory"},{"key":"9459_CR29","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1016\/0097-3165(71)90065-3","volume":"10","author":"RP Stanley","year":"1971","unstructured":"Stanley, R. P.: On the number of open sets of finite topologies. J. Combin. Theory (A) 10, 74\u201379 (1971)","journal-title":"J. Combin. Theory (A)"},{"key":"9459_CR30","volume-title":"Ordered Structures and Partitions","author":"RP Stanley","year":"1971","unstructured":"Stanley, R. P.: Ordered Structures and Partitions. PhD thesis, Harvard (1971)"},{"key":"9459_CR31","doi-asserted-by":"crossref","unstructured":"Stanley, R. P.: Ordered structures and partitions memoirs of the AMS (1972)","DOI":"10.1090\/memo\/0119"},{"key":"9459_CR32","doi-asserted-by":"crossref","unstructured":"Stanley, R. P.: Enumerative combinatorics, 2nd edn, vol. I. Cambridge University Press (2012)","DOI":"10.1017\/CBO9781139058520"},{"key":"9459_CR33","volume-title":"M\u00e4chtigkeiten von Topologien auf endlichen Mengen und Cliquenzahlen in endlichen Graphen","author":"U Vollert","year":"1987","unstructured":"Vollert, U.: M\u00e4chtigkeiten von Topologien auf endlichen Mengen und Cliquenzahlen in endlichen Graphen. University of Hannover, PhD Thesis (1987)"}],"container-title":["Order"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-018-9459-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11083-018-9459-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-018-9459-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,24]],"date-time":"2022-08-24T13:23:47Z","timestamp":1661347427000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11083-018-9459-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,29]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2019,7]]}},"alternative-id":["9459"],"URL":"https:\/\/doi.org\/10.1007\/s11083-018-9459-2","relation":{},"ISSN":["0167-8094","1572-9273"],"issn-type":[{"value":"0167-8094","type":"print"},{"value":"1572-9273","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,29]]},"assertion":[{"value":"27 June 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 April 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 May 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}