On a Speculated Relation Between Chv\'atal-Sankoff Constants of Several Sequences

It is well known that, when normalized by n, the expected length of a longest common subsequence of d sequences of length n over an alphabet of size sigma converges to a constant gamma_{sigma,d}. We disprove a speculation by Steele regarding a possible relation between gamma_{2,d} and gamma_{2,2}. In order to do that we also obtain new lower bounds for gamma_{sigma,d}, when both sigma and d are small integers.Comment: 13 pages. To appear in Combinatorics, Probability and Computin

Long Common Subsequences and the Proximity of Two Random Strings

Let $( x_1 ,x_2 , \cdots x_n )$ and $( x\u27_1 ,x\u27_2 , \cdots x\u27_n , )$ be two strings from an alphabet $mathcal{A}$, and let $L_n$ denote their longest common subsequence. The probabilistic behavior of $L_n$ is studied under various probability models for the x’s and $x\u27$’s