Advanced Counting: Generating Functions and Recurrence Relations

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (26)

Page 1 of 3

Counting with Recurrence Relations: Summary

Explores counting with recurrence relations, linear recurrence relations, generating functions, and counting principles.

Generating Functions: Advanced Counting

Covers the definition of generating functions and their application in solving recurrence relations.

Advanced Counting: Examples

Covers advanced counting techniques, including linear recurrence relations and generating functions, with examples from the Fibonacci sequence and differences between dice and poker cards.

Advanced Counting: Linear Homogeneous Recurrence Relations and Generating Functions

Explores solving linear homogeneous recurrence relations and generating functions for sequence formulas.

Linear Recurrence Relations

Explores linear recurrence relations, including examples like the Fibonacci numbers and the proof of related theorems.

Generating Functions for Correlation Functions

Explores generating functions for correlation functions in the context of the forced harmonic oscillator.

Fibonacci numbers and the golden ratio

Explores the Fibonacci sequence, identities, golden ratio, and explicit formulas.

Extended Binomial Theorem

Explores the Extended Binomial Theorem and counting problems using generating functions.

Ramanujan Graphs: Generating Functions and Expander Graphs

Explores Ramanujan graphs, generating functions, non-backtracking walks, and expander graphs in relation to NP-hard problems.

Generating Functions: Properties and Applications

Explores generating functions, Laplace transform, and their role in probability distributions.