I would like to know why the permutation of the right hand rotor given in Rejewski's paper is $PNP^{-1}$. First of all I can't get how he added an $P$(alphabetic permutation) at the front of $N$(right hand rotor permutation) when there's no alphabetic permutation taking place before the current enters the first rotor permutation. As far as my knowledge goes I think there's only a plugboard swapping that takes place. Second I can't get how an inverse permutation takes place before the current through $N$(right hand rotor permutation) enters the middle hand rotor.
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When ring setting is 01 (A) and indicator shown through the corresponding window is A (01) as well, the wiring core is at its home position. Suppose ring setting is $r$ (variable $r$ not letter $\tt R$) and indicator shown is $s$. Their combined effect is turning the wiring core forward (or counterclockwise when viewing from the right of the machine/rotor) by $n$ places, where $n=(r-1)-(s-1)$ (mod 26). Suppose input letter is $x$. Output letter $y$ is given by $y=(x)P^n N P^{-n}$. If you will allow me to be very verbose on left association, I can write $y = \Big( \big( (x)P^n \big) N \Big) P^{-n}$.