Burnside's lemma

Burnside's Lemma (Part 1) - combining group theory and combinatorics

A result often used in math competitions, Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be transformed into one another by rotation different, like in this cas

From playlist Traditional topics, explained in a new way

Burnside's Lemma (Part 2) - combining math, science and music

Part 1 (previous video): https://youtu.be/6kfbotHL0fs Orbit-stabilizer theorem: https://youtu.be/BfgMdi0OkPU Burnside's lemma is an interesting result in group theory that helps us count things with symmetries considered, e.g. in some situations, we don't want to count things that can be

From playlist Traditional topics, explained in a new way

The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature

In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932

From playlist Algebra

Group theory 10: Burnside's lemma

This is lecture 10 of an online mathematics course on group theory. It introduces Burnside's lemma and uses it to find the number of ways to arrange 8 non-attacking rooks on a chessboard, up to symmetry.

From playlist Group theory

Proof & Explanation: Gauss's Lemma in Number Theory

Euler's criterion: https://youtu.be/2IBPOI43jek One common proof of quadratic reciprocity uses Gauss's lemma. To understand Gauss's lemma, here we prove how it works using Euler's criterion and the Legendre symbol. Quadratic Residues playlist: https://www.youtube.com/playlist?list=PLug5Z

From playlist Quadratic Residues

Maths Problem: Complete Noughts and Crosses (Burnside's Lemma)

How many ways are there to complete a noughts and crosses board - an excuse to show you a little bit of Group Theory. Rotations, reflections and orbits - oh my! Burnside's Lemma http://en.wikipedia.org/wiki/Burnside_lemma Complete sequence https://oeis.org/A082963

From playlist My Maths Videos

Discrete Math II - 10.8.S1 Graphs and Groups: Burnside’s Lemma

This content is not covered in your textbook, but it is an important element in graph coloring. While its roots are in group theory, which we haven't yet learned, we can still benefit from the applications in graph coloring. Video Chapters: Intro 0:00 A Different Kind of Graph Coloring

From playlist Discrete Math II/Combinatorics (entire course)

Rings and midules 3: Burnside ring and rings of differential operators

This lecture is part of an online course on rings and modules. We discuss a few assorted examples of rings. The Burnside ring of a group is a ring constructed form the permutation representations. The ring of differentail operators is a ring whose modules are related to differential equat

From playlist Rings and modules

Theory of numbers: Gauss's lemma

This lecture is part of an online undergraduate course on the theory of numbers. We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Di

From playlist Theory of numbers

Riemann-Lebesgue Lemma

In this video, I prove the famous Riemann-Lebesgue lemma, which states that the Fourier transform of an integrable function must go to 0 as |z| goes to infinity. This is one of the results where the proof is more important than the theorem, because it's a very classical Lebesgue integral

From playlist Real Analysis

Katrin Tent: Burnside groups of relatively small odd exponent

The lecture was held within the framework of the Hausdorff Trimester Program: Logic and Algorithms in Group Theory. Abstract: (joint work with A. Atkarskaya and E. Rips) The free Burnside group B(n,m) of exponent m is the quotient of the free group on n generators by the normal subgroup

From playlist HIM Lectures: Trimester Program "Logic and Algorithms in Group Theory"

An undervalued combinatorial gem: Burnside's lemma | #some1

A little tribute to a favorite theorem, made for SoME1 (https://www.3blue1brown.com/blog/some1). Audio and video can be a second apart at places, I'm not very good at editing yet. Alternate way to fix the faulty 81/8 to get Burnside's lemma (that I realized the day after posting the video

From playlist Summer of Math Exposition Youtube Videos

Discrete Math II - 10.8.S2 Graphs and Groups: Polya's Theorem

This content is also not covered in your textbook, but is another method for graph coloring. In this method, we focus on the number and length of cycles for the permutations that represent each symmetry. Video Chapters: Intro 0:00 Rotations of a Square with Permutations 0:12 Reflectio

From playlist Discrete Math II/Combinatorics (entire course)

Discrete Math II - 10.8.S3 Polya and Burnside: The Chessboard Problem

This final supplement video is just one more practice problem using both Polya's Method and Burnside's Lemma. This example uses a 4X4 chess board in two colors. Video Chapters: Intro 0:00 Chessboard - Burnside 0:14 Burnside Solution 7:21 Chessboard - Polya 7:50 Polya Solution 13:04 Up N

From playlist Discrete Math II/Combinatorics (entire course)

Burnside's Lemma #SoME2

It's spelled 'isomorphism'!

From playlist Summer of Math Exposition 2 videos