Hey! Found your video on the SoME voting page. My process didn't allow me to write official feedback, but I wanted to give you my thoughts anyway. As a combinatorialist, I always think there's more room in this world for lovingly rendered animations to complement combinatorial proofs. The "story" interpretation you used for Bell numbers really fit with this goal. If I had to criticize... without going back to watch the previous video you mentioned, the motivation might be a bit weak? But personally the probability was compelling enough for me. And I don't actually know that I've seen the distribution that you alluded to in the conclusion, so you got my attention there ^_^
The motivation is sort of jokingly weak, I admit! The *real* motivation was when I decided to see what would happen when I computed the inner product of the character of the V= representation of S_n with itself. Too much for a comment--maybe I'll make a video about *that* some time.
Great video and an interesting topic. One small note - music is quite distracting when it abruptly increases in volume when you're not talking, consider keeping it low.
Yes! The formula we derived here only works for m ≤ n, and for a variance computation you'll need the 2nd moment, i.e. m=2. So yes, the variance will be 1 for n at least 2. And in that one case when n=1, the variance is indeed 0.
Hey! Found your video on the SoME voting page. My process didn't allow me to write official feedback, but I wanted to give you my thoughts anyway. As a combinatorialist, I always think there's more room in this world for lovingly rendered animations to complement combinatorial proofs. The "story" interpretation you used for Bell numbers really fit with this goal.
If I had to criticize... without going back to watch the previous video you mentioned, the motivation might be a bit weak? But personally the probability was compelling enough for me. And I don't actually know that I've seen the distribution that you alluded to in the conclusion, so you got my attention there ^_^
The motivation is sort of jokingly weak, I admit! The *real* motivation was when I decided to see what would happen when I computed the inner product of the character of the V= representation of S_n with itself. Too much for a comment--maybe I'll make a video about *that* some time.
Great video and an interesting topic. One small note - music is quite distracting when it abruptly increases in volume when you're not talking, consider keeping it low.
Yeah, sorry about that. Rushed the sound editing to make the #SoME3 deadline just under the wire.
wooooo bijections!!!!
A probability distribution with Bell numbers as its moments? Would that be a Bell curve? :-)
But wait, if n=1, don't we always just get one fixed point? Meaning that the variance is 0?
Yes! The formula we derived here only works for m ≤ n, and for a variance computation you'll need the 2nd moment, i.e. m=2. So yes, the variance will be 1 for n at least 2. And in that one case when n=1, the variance is indeed 0.
Hang on. Did Did use cards for the bell numbers because one of the bell numbers is 52?
Huh...I didn't even notice that. Just a coincidence--like how C(14, 6)=C(15, 5).
@@enumerable345 C(14,6) equals C(15,5) because 10 times 9 equals 15 times 6.