Problem 725

Erdős Problem #725: declared status 'open'. Formalized: no. Give an asymptotic formula for the number of $k\times n$ Latin rectangles. Current best: Yamamoto [Ya51] extended this to $k\leq n^{1/3-o(1)}$. References [ErKa46] Erd\"{o}s, Paul and Kaplansky, Irving, The asymptotic number of Latin rectangles. [Ya51] Yamamoto, Koichi, On the asymptotic number of Latin rectangles. Prize: no. OEIS: A001009. Tags: combinatorics.