The cycle structure of two rows in a random Latin square

@article{Cavenagh2008TheCS,
title={The cycle structure of two rows in a random Latin square},
author={Nicholas J. Cavenagh and Catherine S. Greenhill and Ian M. Wanless},
journal={Random Struct. Algorithms},
year={2008},
volume={33},
pages={286-309}
}

Let L be chosen uniformly at random from among the latin squares of order n ≥ 4 and let r, s be arbitrary distinct rows of L. We study the distribution of σr,s, the permutation of the symbols of L which maps r to s. We show that for any constant c > 0, the following events hold with probability 1− o(1) as n →∞: (i) σr,s has more than (log n)1−c cycles, (ii) σr,s has fewer than 9 √ n cycles, (iii) L has fewer than 9 2n 5/2 intercalates (latin subsquares of order 2). We also show that the… CONTINUE READING