{"language":[{"iso":"eng"}],"doi":"10.1002/rsa.20742","date_created":"2021-06-18T12:47:25Z","extern":"1","status":"public","day":"01","page":"181-196","date_updated":"2023-02-23T14:01:09Z","user_id":"6785fbc1-c503-11eb-8a32-93094b40e1cf","date_published":"2018-03-01T00:00:00Z","title":"Intercalates and discrepancy in random Latin squares","external_id":{"arxiv":["1607.04981"]},"month":"03","abstract":[{"lang":"eng","text":"An intercalate in a Latin square is a 2×2 Latin subsquare. Let N be the number of intercalates in a uniformly random n×n Latin square. We prove that asymptotically almost surely N≥(1−o(1))n2/4, and that EN≤(1+o(1))n2/2 (therefore asymptotically almost surely N≤fn2 for any f→∞). This significantly improves the previous best lower and upper bounds. We also give an upper tail bound for the number of intercalates in two fixed rows of a random Latin square. In addition, we discuss a problem of Linial and Luria on low-discrepancy Latin squares."}],"_id":"9568","article_type":"original","oa_version":"Preprint","intvolume":"        52","article_processing_charge":"No","volume":52,"publication":"Random Structures and Algorithms","oa":1,"publication_identifier":{"issn":["1042-9832"],"eissn":["1098-2418"]},"year":"2018","quality_controlled":"1","publication_status":"published","main_file_link":[{"url":"https://arxiv.org/abs/1607.04981","open_access":"1"}],"scopus_import":"1","citation":{"chicago":"Kwan, Matthew Alan, and Benny Sudakov. “Intercalates and Discrepancy in Random Latin Squares.” <i>Random Structures and Algorithms</i>. Wiley, 2018. <a href=\"https://doi.org/10.1002/rsa.20742\">https://doi.org/10.1002/rsa.20742</a>.","mla":"Kwan, Matthew Alan, and Benny Sudakov. “Intercalates and Discrepancy in Random Latin Squares.” <i>Random Structures and Algorithms</i>, vol. 52, no. 2, Wiley, 2018, pp. 181–96, doi:<a href=\"https://doi.org/10.1002/rsa.20742\">10.1002/rsa.20742</a>.","apa":"Kwan, M. A., &#38; Sudakov, B. (2018). Intercalates and discrepancy in random Latin squares. <i>Random Structures and Algorithms</i>. Wiley. <a href=\"https://doi.org/10.1002/rsa.20742\">https://doi.org/10.1002/rsa.20742</a>","ista":"Kwan MA, Sudakov B. 2018. Intercalates and discrepancy in random Latin squares. Random Structures and Algorithms. 52(2), 181–196.","short":"M.A. Kwan, B. Sudakov, Random Structures and Algorithms 52 (2018) 181–196.","ieee":"M. A. Kwan and B. Sudakov, “Intercalates and discrepancy in random Latin squares,” <i>Random Structures and Algorithms</i>, vol. 52, no. 2. Wiley, pp. 181–196, 2018.","ama":"Kwan MA, Sudakov B. Intercalates and discrepancy in random Latin squares. <i>Random Structures and Algorithms</i>. 2018;52(2):181-196. doi:<a href=\"https://doi.org/10.1002/rsa.20742\">10.1002/rsa.20742</a>"},"publisher":"Wiley","author":[{"full_name":"Kwan, Matthew Alan","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","last_name":"Kwan","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"last_name":"Sudakov","first_name":"Benny","full_name":"Sudakov, Benny"}],"type":"journal_article","issue":"2"}