Re: [math-fun] Re: number of longest common substrings problem

By eye, it appears that the maximum product is always generated by two-element partitions, in which case it further simplifies to selecting 0 <= x <= y <= n such that C(y, x) * C(n-x, n-y) is maximised, which lets me quickly extend the above sequence:

This conjecture appears to be true for large n, but it's not true for all smallish n. For length 4, a non-monotonic pair of strings actually works best: abba and baab, which have 1(aa)+1(bb)+4(ab)+4(ba) = 10 matches. The same is true of 5 and 6. Russ