{"author":[{"last_name":"He","first_name":"Xiaoyu","full_name":"He, Xiaoyu"},{"orcid":"0000-0002-4003-7567","first_name":"Matthew Alan","full_name":"Kwan, Matthew Alan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","last_name":"Kwan"}],"doi":"10.1112/blms.12345","_id":"9573","abstract":[{"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.","lang":"eng"}],"publication_status":"published","publication":"Bulletin of the London Mathematical Society","type":"journal_article","extern":"1","volume":52,"date_updated":"2023-02-23T14:01:23Z","publication_identifier":{"eissn":["1469-2120"],"issn":["0024-6093"]},"external_id":{"arxiv":["1911.12878"]},"page":"515-529","status":"public","oa":1,"user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","article_processing_charge":"No","date_created":"2021-06-21T06:23:42Z","month":"06","citation":{"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>.","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>.","ista":"He X, Kwan MA. 2020. Universality of random permutations. Bulletin of the London Mathematical Society. 52(3), 515–529.","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>"},"title":"Universality of random permutations","quality_controlled":"1","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1911.12878"}],"oa_version":"Preprint","issue":"3","language":[{"iso":"eng"}],"intvolume":"        52","day":"01","article_type":"original","year":"2020","publisher":"Wiley","date_published":"2020-06-01T00:00:00Z"}