Expected length of the longest common subsequence for large alphabets

Abstract

We consider the length L of the longest common subsequence of two randomly uniformly and independently chosen n character words over a k-ary alphabet. Subadditivity arguments yield that E [L] /n converges to a constant γk. We prove a conjecture of Sankoff and Mainville from the early 80's claiming that γk √ k → 2 as k √ ∞. © Springer-Verlag 2004.