Claims

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1946_04_01_erdos_kaplansky: Erdős and Kaplansky (1946) prove that the number of k by n Latin rectangles is asymptotic to e^(-k(k-1)/2) (n!)^k for k below (log n)^(3/2 - epsilon); a partial answer to the problem's request for an asymptotic formula.

1951_01_01_yamamoto: Yamamoto (1951) extends the Erdős–Kaplansky asymptotic for the number of k by n Latin rectangles to every k below n^(1/3 - delta), confirming their conjecture; a partial answer to the problem's request for a formula.

1984_01_01_godsil_mckay: Godsil and McKay (announced 1984, published 1990) prove an asymptotic formula for the number of k by n Latin rectangles for every k = o(n^(6/7)), later claimed for all sublinear k; a partial answer to the problem.

2026_08_03_li: Li's 2026 manuscript stating the Godsil–McKay formula for the number of k by n Latin rectangles for every k = o(n), with a Lean development the author reports as complete; AI-assisted, unreviewed, not refereed.

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