{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T21:30:09Z","timestamp":1768771809503,"version":"3.49.0"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T00:00:00Z","timestamp":1694131200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2024,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that an <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000287_inline1.png\"\/><jats:tex-math>\n$n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-uniform maximal intersecting family has size at most <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0963548323000287_inline2.png\"\/><jats:tex-math>\n$e^{-n^{0.5+o(1)}}n^n$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. This improves a recent bound by Frankl ((2019) <jats:italic>Comb. Probab. Comput.<\/jats:italic><jats:bold>28<\/jats:bold>(5) 733\u2013739.). The Spread Lemma of Alweiss et al. ((2020) <jats:italic>Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing<\/jats:italic>.) plays an important role in the proof.<\/jats:p>","DOI":"10.1017\/s0963548323000287","type":"journal-article","created":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T09:43:03Z","timestamp":1694166183000},"page":"32-49","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["On the size of maximal intersecting families"],"prefix":"10.1017","volume":"33","author":[{"given":"Dmitrii","family":"Zakharov","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,9,8]]},"reference":[{"key":"S0963548323000287_ref12","unstructured":"[12] Rao, A. (2019) Coding for Sunflowers. arXiv preprint arXiv: 1909.04774."},{"key":"S0963548323000287_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcta.2016.11.001"},{"key":"S0963548323000287_ref13","unstructured":"[13] Tao, T. The sunflower lemma via shannon entropy. Available at: https:\/\/terrytao.wordpress.com\/2020\/07\/20\/the-sunflower-lemma-via-shannon-entropy\/."},{"key":"S0963548323000287_ref14","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(94)90108-2"},{"key":"S0963548323000287_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548319000142"},{"key":"S0963548323000287_ref3","first-page":"3","article-title":"On hypergraph cliques with chromatic number 3","volume":"1","author":"Cherkashin","year":"2011","journal-title":"Moscow J. Comb. Number Theory"},{"key":"S0963548323000287_ref7","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1996.0035"},{"key":"S0963548323000287_ref8","unstructured":"[8] Gy\u00e1rf\u00e1s, A. (1977) Partition covers and blocking sets in hypergraphs. MTA SZTAKI Tanulm\u00e1nyok 71."},{"key":"S0963548323000287_ref10","first-page":"125","article-title":"On a problem of Erd\u0151s and Lov\u00e1sz. II. n(r)=O(r)","volume":"7","author":"Kahn","year":"1994","journal-title":"J. Am. Math. Soc."},{"key":"S0963548323000287_ref11","unstructured":"[11] Kupavskii, A. Personal communication."},{"key":"S0963548323000287_ref4","unstructured":"[4] Erd\u0151s, P. and Lov\u00e1sz, L. (1973) Problems and results on 3-chromatic hypergraphs and some related questions. Coll. Math. Soc. Janos Bolyai 10. Infin. Finite Sets, Keszthely (Hungary)."},{"key":"S0963548323000287_ref1","doi-asserted-by":"publisher","DOI":"10.1145\/3357713.3384234"},{"key":"S0963548323000287_ref5","first-page":"3","article-title":"Antichains of fixed diameter","volume":"7","author":"Frankl","year":"2017","journal-title":"Mosc. J. Comb. Number Theory"},{"key":"S0963548323000287_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-17364-6"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548323000287","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,20]],"date-time":"2023-12-20T09:49:20Z","timestamp":1703065760000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548323000287\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,9,8]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,1]]}},"alternative-id":["S0963548323000287"],"URL":"https:\/\/doi.org\/10.1017\/s0963548323000287","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,9,8]]},"assertion":[{"value":"\u00a9 The Author(s), 2023. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}