Does the following make sense?
Let $\sigma\in S_n$ and $\pi\in S_m$. Then sgn$(\sigma\circ\pi)=$sgn$(\sigma)$sgn$(\pi)$.
If it's nonsense, is there any wasy to we split sgn$(\sigma\circ\pi)$?
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1If $n\ne m$, then the composition is not well-defined. – user251257 Oct 17 '17 at 18:04
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If $n=m$, then it is true that $\text{sgn}(\sigma\pi)=\text{sgn}(\sigma)\text{sgn}(\pi)$. – Mike Earnest Oct 17 '17 at 18:07