On Computing the Number of Latin Rectangles

  title={On Computing the Number of Latin Rectangles},
  author={Rebecca J. Stones and Sheng Lin and X. Liu and G. Wang},
  journal={Graphs and Combinatorics},
Doyle (circa 1980) found a formula for the number of $$k \times n$$k×n Latin rectangles $$L_{k,n}$$Lk,n. This formula remained dormant until it was recently used for counting $$k \times n$$k×n Latin rectangles, where $$k \in \{4,5,6\}$$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 $$L_{k,n}$$Lk,n when $$k=4$$k=4 and $$n \le 150$$n≤150, when $$k=5$$k=5 and $$n \le 40$$n≤40 and when $$k=6$$k=6… 

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  • D. Glynn
  • Mathematics
    SIAM J. Discret. Math.
  • 2010
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