Just fyi, as stated the sentence "Therefore c(σ) takes even values if there are evenly many transpositions in σ, and odd values if there are odd-many transpositions in c(σ) is false as stated. It depends on the parity of n --- indeed, c(identity)=n.
Just fyi, as stated the sentence "Therefore c(σ) takes even values if there are evenly many transpositions in σ, and odd values if there are odd-many transpositions in c(σ) is false as stated. It depends on the parity of n --- indeed, c(identity)=n.