The number of Latin rectangles

2007/03/29 by Peter G. Doyle, Doyle, Peter G.
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.math/0703896

Version dated circa 1980; GNU FDL

arxiv created 2007/03/29 · arxiv updated 2009/12/01

Abstract

We show how to generate an expression for the number of k-line Latin rectangles for any k. The computational complexity of the resulting expression, as measured by the number of additions and multiplications required to evaluate it, is on the order of n^(2^(k-1)). These expressions generalize Ryser's formula for derangements.

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