I was recently watching this video on YouTube
https://m.youtube.com/watch?v=qTx98PUW6lE
At timestamp 1:19:05 the lecturer starts talking about a diagramatic representation of permutations that can be represented by connecting three numbers to black/white vertices ( the black/white colour changes the direction of the permutation). He goes on to state that there is a proof that all permutations can be constructed by combining these two basic elements together.
Unfortunately he does not mention the name of this type of representation of permutations. I have tried searching all combinations of keywords I can think of but I can't find more information on this proof, or even this general way of representing permutations.
Could anyone point me in the direction of a website/paper that outlines this proof? I would also be interested to find a resource that talks in detail about this type of representation of permutations. Even the proper name of this type of permuration theory would really help me to find the info I need.
Thanks in advance
Thankyou Berci for that suggestion I was able to find through the references of that book the proof I was looking for. It is in this paper by Postnikov.
https://arxiv.org/abs/math/0609764
Also this type of permutation representation is called 'plabic networks' or 'plabic graphs'.
I look forward to reading the paper!