@article{11186,
  abstract     = {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.},
  author       = {Kwan, Matthew Alan and Sah, Ashwin and Sawhney, Mehtaab},
  issn         = {1469-2120},
  journal      = {Bulletin of the London Mathematical Society},
  number       = {4},
  pages        = {1420--1438},
  publisher    = {Wiley},
  title        = {{Large deviations in random latin squares}},
  doi          = {10.1112/blms.12638},
  volume       = {54},
  year         = {2022},
}