Al Aho tells me that the problem he is interested in is to find the maximum number of longest common subsequences of two sequences X and Y of length n, without regard to where the subsequence occurs in X and Y. So for X = aabaa, Y =Â aaabb, the length of the lcs is 3, and there are two subsequences of length 3 that are possible, aaa and aab. So here F(X,Y) = 2. Some definitions: S is a subsequence of X if S can be obtained by deleting some of the entries of X (not necessarily adjacent). S is a longest common subsequence of X and Y if S is a subsequence of X, S is a subsequence of Y, and there is no T such that S subsequence of T, S not equal T, and T is a subsequence of X, T is a subsequence of Y. Given sequences X and Y of length n, let LCS(X,Y) be the length of the longest common subsequence. Let F(X,Y) = no of sequences S such that S is a longest common subsequence of X and Y. So S has length LCS(X,Y). Given n, what is the maximal value of F(X,Y) over all choices of X and Y over any alphabet? The version of the problem that i stated earlier, where you also take into account the location of S inside X and Y, is also interesting, it is just not Al's original question. NJAS