Large deviations in random latin squares Kwan, Matthew Alan ; https://orcid.org/0000-0002-4003-7567 Sah, Ashwin Sawhney, Mehtaab ddc:510 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. Wiley 2022 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/11186 https://research-explorer.ista.ac.at/download/11186/12499 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> eng info:eu-repo/semantics/altIdentifier/doi/10.1112/blms.12638 info:eu-repo/semantics/altIdentifier/issn/0024-6093 info:eu-repo/semantics/altIdentifier/e-issn/1469-2120 info:eu-repo/semantics/altIdentifier/wos/000779920900001 info:eu-repo/semantics/altIdentifier/arxiv/2106.11932 info:eu-repo/semantics/openAccess