Most Latin Squares Have Many Subsquares

@article{McKay1999MostLS,
  title={Most Latin Squares Have Many Subsquares},
  author={Brendan D. McKay and Ian M. Wanless},
  journal={J. Comb. Theory, Ser. A},
  year={1999},
  volume={86},
  pages={323-347}
}
A k_n Latin rectangle is a k_n matrix of entries from [1, 2, ..., n] such that no symbol occurs twice in any row or column. An intercalate is a 2_2 Latin subrectangle. Let N(R) be the number of intercalates in R, a randomly chosen k_n Latin rectangle. We obtain a number of results about the distribution of N(R) including its asymptotic expectation and a bound on the probability that N(R)=0. For =>0 we prove most Latin squares of order n have N(R) n . We also provide data from a computer… CONTINUE READING

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