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Consider the set of numbers $N = \{ 1, \dots, n \}$ and let $S \subseteq N$ be a subset.

Now let $\pi : N \rightarrow N$ be bijective, so $\pi$ is a permutation of the numbers from $1$ to $n$.

Then $\pi(S) \subset N$ is another subset, and generally the permutation will not list the elements of $S$ in the correct order. What is the sign of the permutation over $\pi(S)$ that orders them back?

shuhalo
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1 Answers1

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If $S=\{m_1,m_2,\dots,m_k\}\subseteq N$, then we can write $$\pi(S) = \{\pi(m_1),\pi(m_2),\dots,\pi(m_k)\}.$$

Worachead Sommanee
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