@article{9568,
abstract = {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.},
author = {Kwan, Matthew Alan and Sudakov, Benny},
issn = {1098-2418},
journal = {Random Structures and Algorithms},
number = {2},
pages = {181--196},
publisher = {Wiley},
title = {{Intercalates and discrepancy in random Latin squares}},
doi = {10.1002/rsa.20742},
volume = {52},
year = {2018},
}