Next, we'll just talk about a few exercises that you might do to test your

understanding of, of this material. as promised let's do an exercise where

you apply the general methodology for enumerating strings not containing

particular patterns. And so this is just a plug and chug from

one of the slides involving correlation polynomial to get the generating function

for the strings that do not contain say a pattern with nine 0s and a 1.

Or alternating 0s and 1s. and then, once you get that generating

function, apply the metamorphic transfer theorem to get the coefficient

asymptotics. for a second exercise.

try taking a look at the applying the theorem for super critical sequence

classes to study parameters in variations of the basic classes that I talked about.

For example, compositions of 1s, 2s and 3s or triple surjections or alignments

with no singleton cycles. So, you can numerate and get the number

of parts in a random object for all of those things very easily with the super

critical sequence schema. so as usual read the corresponding

chapter in the text. but there's quite a bit of advanced

material that most people will want to scheme at this point.

with the usual idea that you try to get a feeling for what's there, not understand

really every detail. and then, write up solutions to those

exercises, definitely worth doing. and then, as our programming exercise

that is entertaining. go ahead and use the plot code that's

posted on the web. that you did for the last lecture.

And plot the GF's for the sets of bit strings that you considered in the first

web exercises for the ones having no occurrence of all 0s followed by a 1.

And the 1s for alternating 0s and 1s. Now, those are just a few assignments

that, you know, you might do to check your understanding of the material in

this lecture.