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