{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T19:25:37Z","timestamp":1769023537803,"version":"3.49.0"},"reference-count":12,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,12,4]],"date-time":"2018-12-04T00:00:00Z","timestamp":1543881600000},"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":[[2019,11]]},"DOI":"10.1007\/s11083-018-9480-5","type":"journal-article","created":{"date-parts":[[2018,12,3]],"date-time":"2018-12-03T21:20:18Z","timestamp":1543872018000},"page":"507-510","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["A Simple Upper Bound on the Number of Antichains in [t]n"],"prefix":"10.1007","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1328-8149","authenticated-orcid":false,"given":"Shen-Fu","family":"Tsai","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,12,4]]},"reference":[{"key":"9480_CR1","unstructured":"Carroll, T., Cooper, J., Tetali, P.: Counting antichains and linear extensions in generalizations of the boolean lattice (2009)"},{"key":"9480_CR2","first-page":"1","volume-title":"Fest-Schrift der Herzoglichen Technischen Hochschule Carolo-Wilhelmina","author":"R. Dedekind","year":"1897","unstructured":"Dedekind, R.: \u00dcber Zerlegungen Von Zahlen Durch Ihre Gr\u00f6ssten Gemeinsamen Theiler. In: Fest-Schrift Der Herzoglichen Technischen Hochschule Carolo-Wilhelmina, pp. 1\u201340. Springer (1897)"},{"issue":"1","key":"9480_CR3","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/0097-3165(76)90079-0","volume":"20","author":"C Greene","year":"1976","unstructured":"Greene, C., Kleitman, D.J.: Strong versions of sperner\u2019s theorem. Journal of Combinatorial Theory, Series A 20(1), 80\u201388 (1976)","journal-title":"Journal of Combinatorial Theory, Series A"},{"issue":"20","key":"9480_CR4","first-page":"1088","volume":"262","author":"G Hansel","year":"1966","unstructured":"Hansel, G.: Sur le nombre des fonctions bool\u00e9ennes monotones de n variables. Comptes rendus hebdomadaires des s\u00e9ances de l\u2019acad\u00e9mie des sciences. S\u00e9rie A 262(20), 1088 (1966)","journal-title":"Comptes rendus hebdomadaires des s\u00e9ances de l\u2019acad\u00e9mie des sciences. S\u00e9rie A"},{"issue":"2","key":"9480_CR5","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1090\/S0002-9939-01-06058-0","volume":"130","author":"J Kahn","year":"2002","unstructured":"Kahn, J.: Entropy, independent sets and antichains: a new approach to dedekind\u2019s problem. Proc. Am. Math. Soc. 130(2), 371\u2013378 (2002)","journal-title":"Proc. Am. Math. Soc."},{"issue":"1","key":"9480_CR6","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1016\/0095-8956(72)90033-0","volume":"12","author":"G Katona","year":"1972","unstructured":"Katona, G.: A generalization of some generalizations of sperner\u2019s theorem. Journal of Combinatorial Theory, Series B 12(1), 72\u201381 (1972)","journal-title":"Journal of Combinatorial Theory, Series B"},{"key":"9480_CR7","first-page":"373","volume":"213","author":"DJ Kleitman","year":"1975","unstructured":"Kleitman, D.J., Markowsky, G.: On dedekind\u2019s problem: the number of isotone boolean functions. ii. Trans. Am. Math. Soc. 213, 373\u2013390 (1975)","journal-title":"Trans. Am. Math. Soc."},{"key":"9480_CR8","first-page":"5","volume":"38","author":"AD Korshunov","year":"1981","unstructured":"Korshunov, A.D.: On the number of monotone boolean menge. Problemy kibernetiki 38, 5\u2013109 (1981)","journal-title":"Problemy kibernetiki"},{"issue":"17","key":"9480_CR9","doi-asserted-by":"publisher","first-page":"2992","DOI":"10.1016\/j.spl.2008.05.005","volume":"78","author":"L Mattner","year":"2008","unstructured":"Mattner, L., Roos, B.: Maximal probabilities of convolution powers of discrete uniform distributions. Statist. Probab. Lett. 78(17), 2992\u20132996 (2008)","journal-title":"Statist. Probab. Lett."},{"key":"9480_CR10","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.1016\/j.aim.2014.06.008","volume":"262","author":"G Moshkovitz","year":"2014","unstructured":"Moshkovitz, G., Shapira, A.: Ramsey theory, integer partitions and a new proof of the erd\u00f6s\u2013szekeres theorem. Adv. Math. 262, 1107\u20131129 (2014)","journal-title":"Adv. Math."},{"issue":"6","key":"9480_CR11","doi-asserted-by":"publisher","first-page":"2096","DOI":"10.1109\/18.782146","volume":"45","author":"H Pippenger","year":"1999","unstructured":"Pippenger, H.: Entropy and enumeration of boolean functions. IEEE Trans. Inf. Theory 45(6), 2096\u20132100 (1999)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"1","key":"9480_CR12","first-page":"74","volume":"1","author":"AA Sapozhenko","year":"1989","unstructured":"Sapozhenko, A.A.: The number of antichains in ranked partially ordered sets. Diskretnaya Matematika 1(1), 74\u201393 (1989)","journal-title":"Diskretnaya Matematika"}],"container-title":["Order"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-018-9480-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11083-018-9480-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11083-018-9480-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T19:08:15Z","timestamp":1575400095000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11083-018-9480-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,4]]},"references-count":12,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,11]]}},"alternative-id":["9480"],"URL":"https:\/\/doi.org\/10.1007\/s11083-018-9480-5","relation":{},"ISSN":["0167-8094","1572-9273"],"issn-type":[{"value":"0167-8094","type":"print"},{"value":"1572-9273","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,4]]},"assertion":[{"value":"7 June 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 November 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 December 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}