Explore
For Enterprise
Join for Free
Log In

Browse
Search
For Enterprise
Log In
Join for Free

Exercises

Loading...

Analytic Combinatorics

Princeton University

4.7 (26 ratings) | 13K Students Enrolled

Analytic Combinatorics teaches a calculus that enables precise quantitative predictions of large combinatorial structures. This course introduces the symbolic method to derive functional relations among ordinary, exponential, and multivariate generating functions, and methods in complex analysis for deriving accurate asymptotics from the GF equations. All the features of this course are available for free. It does not offer a certificate upon completion.

Reviews

4.7 (26 ratings)

5 stars
22 ratings
4 stars
2 ratings
3 stars
1 ratings
2 stars
1 ratings

From the lesson

Applications of Singularity Analysis

We see how the Flajolet-Odlyzko approach leads to universal laws covering combinatorial classes built with the set, multiset, and recursive sequence constructions. Then we consider applications to many of the classic combinatorial classes that we encountered in Lectures 1 and 2.

Simple Varieties of Trees16:01

Labelled Sets 15:37

Tree-like Classes 16:47

Taught By

Robert Sedgewick
William O. Baker *39 Professor of Computer Science

Transcript

now for exercises to test your understanding of this. remember I left for an exercise, applying the tree-like schema theorem to develop an asymptotic expression for the number of bracketings within leaves. That's Schroder's second problem. That's an interesting problem and you can read more about it on page 69 of the book and on page 474. the note on page 474 uses a different method to derive the result. so, you'll see for your exercise when you use the treelike schema that, you get out to the same result. and so that's a, a worthwhile problem to work to, understand how, how to apply treelike schema. in that, just that one exercise because, there were, others, in the last lecture which is the same week as this one. and again, take a look at the text, and again, particularly in this case, there is quite a bit there that I didn't cover in this lecture. Mostly around calculating the constant for context free and proving some of these theorems and schema, which is not what we are doing in this introductory treatment The next course in analytic combinatorics, we're going to talk about some of these books set and extensions. In write up solutions table, that exercise for solving numbers. and it's worthwhile as long as you have the code to do data plots from the last couple of lectures. Do our data plot of bracketing to see what that generate function looks like in complex plane. So those are the exercises for application of singularity analysis.

Explore our Catalog

Join for free and get personalized recommendations, updates and offers.

Coursera provides universal access to the world’s best education, partnering with top universities and organizations to offer courses online.

© 2019 Coursera Inc. All rights reserved.

Get it on Google Play

Coursera
About
Leadership
Careers
Catalog
Certificates
MasterTrack™ Certificates
Degrees
For Enterprise
For Government
For Campus

Community
Learners
Partners
Developers
Beta Testers
Translators

Connect
Blog
Facebook
LinkedIn
Twitter
Instagram
YouTube
Tech Blog

More
Terms
Privacy
Help
Accessibility
Press
Contact
Directory
Affiliates