# 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} }

- Published in Graphs and Combinatorics 2016
DOI:10.1007/s00373-015-1643-1

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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