Today I had the problem of knowing in how many ways a string or sequence can be splitted. I found that many things are written in mathematics about partitions. For example, the ordered partition of a set is very close to what I was looking for. Also, there are many curious things about integer partitions, but I was not able to find the answer to my problem.

Finally, by an intuitive graphic proff, I found that 2^(n-1) was the size of all possible partitions of a sequence of length n.

The problem is supposed to be simple. Though I found the answer, I still feel a bit frustated of not been able to find it by combinatorics theory.