So that's a t restricted tree.

And then there's something called the 2-3 tree which is actually the method of

choice in symbol-table implementations and that also generalizes to multiple.

And that's where you can have more than one key per node.

It's kind of a strange structure, but actually

It's easy to represent as a binary tree and I'll show that in a second.

And again, all of these are going to give rise to enumeration problems for any value

of p, path length and all sorts of other things that we might want to analyze.

All these different variations just so far we've talked about 12 different types

of trees and more emphasize the need why we

need general tools like analytic combinatorics that can get

us the solutions to problems without necessarily going into the details.

It's why we need the general theorems that we've talked about a little bit and

we're going to talk about more later.

You can already easily see how easy it is to specify structures like this.

I'm not writing it down here but you can certainly take

the defining construction for binary trees and

extend that to do ternary trees or fournary trees.

And now you know that if you can do that then you have a generating

function equation.

Now a lot of these generating function equations are not as simple to solve or

get asymptotics for as the but we will learn techniques for that.

But at least I think people in the course are convinced that we can get

to generating functions pretty quickly for all of these types of structures.