Last lecture when we’re looking at strings we're concerned about the sequence

of characters and about the relationship between one and the next in the sequence.

Looking for patterns in the string so forth.

This time,

we're interested in applications where the sets of indices are important.

Where it matters how many zeros there are.

How many ones there are.

And so forth.

But really, it's the same object.

And strings where were using OGFs to enumerate.

Words that we're going to use.

So that's a difference in point of view,

and a difference in technique that we use to analyze variations.

So again, here's just a summary for strings, which we considered last time.

Considered them as unlabeled objects, we used OGF to enumerate them.

Typical string is just a sequence of characters, so

the OGF is 1 / 1- Mz if there is M characters, those M to the interval.

For words, we consider them as labelled objects and

use an EGF and we had all these different representations.

And now when we're doing sequence, we're doing star product,

where we're relatable in all possible ways.

And our number of different words is E to the N Z, but we get the same result out.

So, we're going to be focusing on the kind of representation in this lecture.