Theory of Symmetric Groups

[anshwad10]

No description provided.

[anshwad10]

#1186

[marcinjangrzybowski]

@anshwad10 I have lots of unpublisehd code on finite permutations, and also finitely generated permutations of Nat,
let me knwo if you need any concrete resullts related to those, and I can clear it up enogught to make PR. you an reach me at [email protected]

[anshwad10]

Have you defined the parity of a permutation and proved that it is a group homomorphism to BoolGroup?

[marcinjangrzybowski]

yes:
https://github.com/marcinjangrzybowski/cubical/blob/b8b0fb53064db0b630dd1b0456a6396eddb98953/Cubical/Data/FinData/Transpositions.agda#L245-L250

also
abelianization of braid group 𝐵𝑛 , for 𝑛≥2 is isomorphic to ℤ

[marcinjangrzybowski]

this is really dirty code thru, full fo different experiments, do not bother readinig itbefore I will celan it up, but ddefintely can extract enough to get those result by the end of the weekend

[marcinjangrzybowski]

it is using my old presented-group machinery, I have new verision, need to merge those two, so I again caution you to not read too much into this version :)