--- res: bibo_abstract: - 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.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Xiaoyu foaf_name: He, Xiaoyu foaf_surname: He - foaf_Person: foaf_givenName: Matthew Alan foaf_name: Kwan, Matthew Alan foaf_surname: Kwan foaf_workInfoHomepage: http://www.librecat.org/personId=5fca0887-a1db-11eb-95d1-ca9d5e0453b3 orcid: 0000-0002-4003-7567 bibo_doi: 10.1112/blms.12345 bibo_issue: '3' bibo_volume: 52 dct_date: 2020^xs_gYear dct_isPartOf: - http://id.crossref.org/issn/0024-6093 - http://id.crossref.org/issn/1469-2120 dct_language: eng dct_publisher: Wiley@ dct_title: Universality of random permutations@ ...