{"status":"public","day":"01","main_file_link":[{"url":"https://arxiv.org/abs/1911.12878","open_access":"1"}],"publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"date_published":"2020-06-01T00:00:00Z","external_id":{"arxiv":["1911.12878"]},"quality_controlled":"1","publication":"Bulletin of the London Mathematical Society","issue":"3","language":[{"iso":"eng"}],"article_processing_charge":"No","publisher":"Wiley","abstract":[{"lang":"eng","text":"It is a classical fact that for any ε>0, a random permutation of length n=(1+ε)k2/4 typically contains a monotone subsequence of length k. As a far-reaching generalization, Alon conjectured that a random permutation of this same length n is typically k-universal, meaning that it simultaneously contains every pattern of length k. He also made the simple observation that for n=O(k2logk), a random length-n permutation is typically k-universal. We make the first significant progress towards Alon's conjecture by showing that n=2000k2loglogk suffices."}],"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","scopus_import":"1","doi":"10.1112/blms.12345","citation":{"apa":"He, X., &#38; Kwan, M. A. (2020). Universality of random permutations. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.12345\">https://doi.org/10.1112/blms.12345</a>","short":"X. He, M.A. Kwan, Bulletin of the London Mathematical Society 52 (2020) 515–529.","mla":"He, Xiaoyu, and Matthew Alan Kwan. “Universality of Random Permutations.” <i>Bulletin of the London Mathematical Society</i>, vol. 52, no. 3, Wiley, 2020, pp. 515–29, doi:<a href=\"https://doi.org/10.1112/blms.12345\">10.1112/blms.12345</a>.","ista":"He X, Kwan MA. 2020. Universality of random permutations. Bulletin of the London Mathematical Society. 52(3), 515–529.","ama":"He X, Kwan MA. Universality of random permutations. <i>Bulletin of the London Mathematical Society</i>. 2020;52(3):515-529. doi:<a href=\"https://doi.org/10.1112/blms.12345\">10.1112/blms.12345</a>","ieee":"X. He and M. A. Kwan, “Universality of random permutations,” <i>Bulletin of the London Mathematical Society</i>, vol. 52, no. 3. Wiley, pp. 515–529, 2020.","chicago":"He, Xiaoyu, and Matthew Alan Kwan. “Universality of Random Permutations.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2020. <a href=\"https://doi.org/10.1112/blms.12345\">https://doi.org/10.1112/blms.12345</a>."},"type":"journal_article","year":"2020","author":[{"first_name":"Xiaoyu","last_name":"He","full_name":"He, Xiaoyu"},{"orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","last_name":"Kwan","full_name":"Kwan, Matthew Alan"}],"title":"Universality of random permutations","_id":"9573","volume":52,"date_updated":"2023-02-23T14:01:23Z","page":"515-529","month":"06","date_created":"2021-06-21T06:23:42Z","extern":"1","intvolume":"        52","article_type":"original","publication_status":"published","oa":1,"oa_version":"Preprint"}