Dixon's Identity
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- Опубликовано: 10 июн 2024
- We prove Dixon's Identity using an elementary sign-reversing involution with exceptions. We also give combinatorial interpretations for binomial and trinomial coefficients. #combinatorics #involution #math
The D.I.E. technique: • Proofs to D.I.E. For
Discussion of a combinatorial proof of Dixon's Identity: math.stackexchange.com/questi...
Music: Boreal - Asher Falero
Timestamps:
0:00 - Introduction
0:33 - D.I.E Recap
1:20 - Attribution
1:45 - Trinomial Coefficients
4:18 - Trinomial D.I.E. proof
5:42 - Triple-paths
7:45 - Dixon's Identity: Description
10:56 - Dixon's Identity: Involution
12:46 - Dixon's Identity: Exceptions
13:33 - Outro
Holy cow, this is a criminally under-subscribed channel.
Another vid, another banger 😮💨
No idea what I am watching, looks pretty though 🥺
love your work.
Brilliant ...
It won't be wrong to call you Grant Sanderson of combinatorics (but I appreciate you as a unique individual and your efforts and time that you put to beautifully simplify maths)
Should we expect to get a full playlist on combinatorics by you?
So kind, thanks! I definitely have ideas for a few more videos.
Very cool video, I love sign reversing involutions
Very very nice
Me in my combinatorial class: DIE
Underrated 😂
I love homological combinatorics
Remove logical combinatorics lol
What software is he using to write the formulas and animate them ? Manim ?
Yep, Manim for everything!
I was here at 1k subscribers and less than 5k views.
These trinomial coefficients... (a+b+c a,b,c)=(a+b+c a)*(b+c b). This can be used to make many identities, such as the Team-Leader identity from the derangement video i think?
There are indeed tons of analogous identities/proofs with trinomial coefficients.
i would rather DIE than count
Matching is so much easier than counting!