How many possibilities are there for dividing a string to substrings, of any length?

Hi.

I just can wrap my head around this.

Let S be a string of length n:

how many possibilities are there for dividing it to substrings?

for example:

is one division, and:

is another.

how many like that are there?

I can't think of anything and could really use some help here.

Thanks in anvanced!

Re: How many possibilities are there for dividing a string to substrings, of any leng

Never mind...

found it.

It's

Re: How many possibilities are there for dividing a string to substrings, of any leng

Re: How many possibilities are there for dividing a string to substrings, of any leng

Hi Plato, thanks for the help.

according to what you're saying, it's , which is .

Re: How many possibilities are there for dividing a string to substrings, of any leng

Quote:

Originally Posted by

**Stormey** according to what you're saying, it's

, which is

.

**Yes exactly**.

It is well known that .

That is the number of subsets of a set of N elements.