On Computing the Number of Latin Rectangles

Rebecca J. Stones, Sheng Lin, Xiaoguang Liu, Gang Wang
2015 Graphs and Combinatorics  
Doyle (circa 1980) found a formula for the number of k ×n Latin rectangles L k,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 L k,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 about the divisors of L k,n are presented.
doi:10.1007/s00373-015-1643-1 fatcat:w4ngciaofzdidp2ouapvrbecxq