On Computing the Number of Latin Rectangles

@article{Stones2016OnCT,
  title={On Computing the Number of Latin Rectangles},
  author={Rebecca J. Stones and Sheng Lin and Xiaoguang Liu and Gang Wang},
  journal={Graphs and Combinatorics},
  year={2016},
  volume={32},
  pages={1187-1202}
}
Doyle (circa 1980) found a formula for the number of k×n Latin rectangles Lk,n . This formula remained dormant until it was recently used for counting k × n Latin rectangles, where k ∈ {4, 5, 6}. We give a formal proof of Doyle’s formula for arbitrary k. We also improve a previous implementation of this formula, which we use to find Lk,n when k = 4 and n ≤ 150, when k = 5 and n ≤ 40 and when k = 6 and n ≤ 15. Motivated by computational data for 3 ≤ k ≤ 6, some research problems and conjectures… CONTINUE READING
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SHOWING 1-10 OF 45 REFERENCES

Divisors of the number of Latin rectangles

  • J. Comb. Theory, Ser. A
  • 2010
VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

On the number of Latin rectangles

D S.Stones
  • Ph.D. thesis, Monash University
  • 2010
VIEW 6 EXCERPTS
HIGHLY INFLUENTIAL

The Many Formulae for the Number of Latin Rectangles

  • Electr. J. Comb.
  • 2010
VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

The Riordan generalized formula for three-line Latin rectangles and its applications

V. S. Shevelev
  • DAN of the Ukraine 2, 8–12
  • 1991
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Formulae for the Alon-Tarsi Conjecture

  • SIAM J. Discrete Math.
  • 2012
VIEW 1 EXCERPT

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