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
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Showing 1-10 of 17 references

Random graphs

V. F. Kolchin
Cambridge University Press, Cambridge • 1999
View 2 Excerpts
Highly Influenced

An introduction to quasigroups and their representations

J.D.H. Smith
Chapman & Hall/CRC, Boca Raton, FL • 2007
View 1 Excerpt

Cycle Switches in Latin Squares

Graphs and Combinatorics • 2004

Most Latin Squares Have Many Subsquares

J. Comb. Theory, Ser. A • 1999
View 3 Excerpts

Generating uniformly distributed random latin squares

M. T. Jacobson, P. Matthews
J. Combin. Des. 4, • 1996
View 2 Excerpts

Generatingfunctionology (2nd edn.)

H. S. Wilf
1994