On a textbook, the wedge product of the covectors $\Omega$ is spanned on basis vectors $dx$ using this notation. $$\Omega^i=\Omega^i_\mu dx^{\mu}$$ $i$ is the name of the covector, not an index.
$$\Omega^1\wedge\Omega^2\cdots\wedge\Omega^p=\Omega^1_{i_1}dx^{i_1}\wedge\Omega^2_{i_2}dx^{i_2}\wedge\cdots\wedge\Omega^p_{i_p}dx^{i_p}=$$
$$=\omega^1_{i_1}\omega^2_{i_2}\omega^p_{i_p}dx^{i_1}\wedge dx^{i_2}\wedge\cdots\wedge dx^{i_p}=$$ $$=\underset{i_1<i_2\cdots<i_p}{\sum}\underset{\sigma} {\sum}\Omega^1_{\sigma(i_1)}\Omega^2_{\sigma(i_2)}\cdots \Omega^p_{\sigma(i_p)}dx^{i_1}\wedge dx^{i_2}\wedge\cdots\wedge dx^{i_p}$$
I don't understand why is the summation taken over the ascending sequence of $i$.