Hi,

I'm looking for a problem of finding the length of the k-th longest common subsequences. The subsequences can be increasing, or alternative, or having no matter what kind of other properties are required or not. The limiting law of the length of the k-th longest increasing subsequences has been studied a lot (arbitrary distribution, nonasymptotically, the sequences/words are assumed to be generated from a distribution). But for the "common" version, I didn't find an analog even limited to uniformly distributed binary words. (Finding the length of the increasing subseq of a binary string looks quite weird, but some people worked on it anyway...)

I asked some math people working in this field, but they never saw papers like this. I am wondering if there is any OJ problem (since research and programming contests sometimes have gaps...) Did anyone see one that requires a "k-th" and "common" subsequence? Thanks!!