{"has_accepted_license":"1","isi":1,"abstract":[{"text":"In this note, we study large deviations of the number  𝐍  of intercalates ( 2×2  combinatorial subsquares which are themselves Latin squares) in a random  𝑛×𝑛  Latin square. In particular, for constant  𝛿>0  we prove that  exp(−𝑂(𝑛2log𝑛))⩽Pr(𝐍⩽(1−𝛿)𝑛2/4)⩽exp(−Ω(𝑛2))  and  exp(−𝑂(𝑛4/3(log𝑛)))⩽Pr(𝐍⩾(1+𝛿)𝑛2/4)⩽exp(−Ω(𝑛4/3(log𝑛)2/3)) . As a consequence, we deduce that a typical order- 𝑛  Latin square has  (1+𝑜(1))𝑛2/4  intercalates, matching a lower bound due to Kwan and Sudakov and resolving an old conjecture of McKay and Wanless.","lang":"eng"}],"type":"journal_article","license":"https://creativecommons.org/licenses/by-nc/4.0/","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file_date_updated":"2023-02-03T09:43:38Z","publisher":"Wiley","day":"01","ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by-nc/4.0/legalcode","short":"CC BY-NC (4.0)","image":"/images/cc_by_nc.png","name":"Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)"},"oa":1,"title":"Large deviations in random latin squares","intvolume":"        54","article_processing_charge":"No","doi":"10.1112/blms.12638","citation":{"mla":"Kwan, Matthew Alan, et al. “Large Deviations in Random Latin Squares.” <i>Bulletin of the London Mathematical Society</i>, vol. 54, no. 4, Wiley, 2022, pp. 1420–38, doi:<a href=\"https://doi.org/10.1112/blms.12638\">10.1112/blms.12638</a>.","ista":"Kwan MA, Sah A, Sawhney M. 2022. Large deviations in random latin squares. Bulletin of the London Mathematical Society. 54(4), 1420–1438.","short":"M.A. Kwan, A. Sah, M. Sawhney, Bulletin of the London Mathematical Society 54 (2022) 1420–1438.","chicago":"Kwan, Matthew Alan, Ashwin Sah, and Mehtaab Sawhney. “Large Deviations in Random Latin Squares.” <i>Bulletin of the London Mathematical Society</i>. Wiley, 2022. <a href=\"https://doi.org/10.1112/blms.12638\">https://doi.org/10.1112/blms.12638</a>.","ieee":"M. A. Kwan, A. Sah, and M. Sawhney, “Large deviations in random latin squares,” <i>Bulletin of the London Mathematical Society</i>, vol. 54, no. 4. Wiley, pp. 1420–1438, 2022.","ama":"Kwan MA, Sah A, Sawhney M. Large deviations in random latin squares. <i>Bulletin of the London Mathematical Society</i>. 2022;54(4):1420-1438. doi:<a href=\"https://doi.org/10.1112/blms.12638\">10.1112/blms.12638</a>","apa":"Kwan, M. A., Sah, A., &#38; Sawhney, M. (2022). Large deviations in random latin squares. <i>Bulletin of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/blms.12638\">https://doi.org/10.1112/blms.12638</a>"},"date_published":"2022-08-01T00:00:00Z","external_id":{"isi":["000779920900001"],"arxiv":["2106.11932"]},"quality_controlled":"1","article_type":"original","_id":"11186","status":"public","department":[{"_id":"MaKw"}],"author":[{"full_name":"Kwan, Matthew Alan","last_name":"Kwan","first_name":"Matthew Alan","orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3"},{"first_name":"Ashwin","full_name":"Sah, Ashwin","last_name":"Sah"},{"first_name":"Mehtaab","last_name":"Sawhney","full_name":"Sawhney, Mehtaab"}],"publication":"Bulletin of the London Mathematical Society","acknowledgement":"We thank Zach Hunter for pointing out some important typographical errors. We also thank the referee for several remarks which helped improve the paper substantially.\r\nKwan was supported by NSF grant DMS-1953990. Sah and Sawhney were supported by NSF Graduate Research Fellowship Program DGE-1745302.","page":"1420-1438","language":[{"iso":"eng"}],"issue":"4","year":"2022","volume":54,"publication_identifier":{"issn":["0024-6093"],"eissn":["1469-2120"]},"date_created":"2022-04-17T22:01:48Z","date_updated":"2023-08-03T06:47:29Z","month":"08","file":[{"success":1,"file_id":"12499","checksum":"02d74e7ae955ba3c808e2a8aebe6ef98","content_type":"application/pdf","file_name":"2022_BulletinMathSociety_Kwan.pdf","relation":"main_file","file_size":233758,"creator":"dernst","access_level":"open_access","date_created":"2023-02-03T09:43:38Z","date_updated":"2023-02-03T09:43:38Z"}],"publication_status":"published","oa_version":"Published Version","scopus_import":"1"}