Every mathematician has seen the burnside lemma at some point in their careers (because it is part of the standard curriculum of math), but I am sure that many of them won't remember the precise statement... Having a good easy example in mind would help people to remember it (unfortunately, many lecturers just go about talking group actions and prove the result without giving concrete examples)... So, great job at giving a good concrete example! Although it is true that you only mention burnside lemma at the end, i think that the video does a good job explaining the main idea, and also makes people curious about this type of math... To make it even more concrete, can you think of an algorithm that would list all possible necklaces? how efficient that algorithm would be and how it would generalize if you have some other forms of symmetries? BTW, i believe that in math, necklaces refer to the case in which you have rotational symmetry, and Bracelets (or turnover/free necklace) for the case in which you also have reflection symmetry (but it is okay since you explain what you meant by necklace)
Loved the video, (I'm judging this one), but for a video to have "Burnside's Lemma" in the title, it only went into it very shallowly at the end.
I just wanted to get a necklace for my mom
Great, but with 3 colors, you get 39 necklaces (5 beads), not 30. Time 12:50
thanks alot!
Every mathematician has seen the burnside lemma at some point in their careers (because it is part of the standard curriculum of math), but I am sure that many of them won't remember the precise statement... Having a good easy example in mind would help people to remember it (unfortunately, many lecturers just go about talking group actions and prove the result without giving concrete examples)... So, great job at giving a good concrete example! Although it is true that you only mention burnside lemma at the end, i think that the video does a good job explaining the main idea, and also makes people curious about this type of math...
To make it even more concrete, can you think of an algorithm that would list all possible necklaces? how efficient that algorithm would be and how it would generalize if you have some other forms of symmetries?
BTW, i believe that in math, necklaces refer to the case in which you have rotational symmetry, and Bracelets (or turnover/free necklace) for the case in which you also have reflection symmetry (but it is okay since you explain what you meant by necklace)
good. pls make more....