The Asymptotic Number of Latin Rectangles

Abstract

1. Introduction. The problem of enumerating n by k Latin rectangles was solved formally by MacMahon [4] using his operational methods. For k = 3, more explicit solutions have been given in [1], [2], [3], and [5]. Wile further exact enumeration seems difficult, it is an easy heuristic conjecture that the number of n by k Latin rectangles is asymptotic to