[Jprogramming] Permutations, primes and modular arithmetic

[Jimmy Gauvin]

Hi,

I am looking for some reference texts on permutations and modular
arithmetic.

I recently stumbled on some interesting properties of card shuffles.
For example, using a deck of 11 cards labeled 0 through 10 and shuffling
them to obtain this layout :

   0  6  1  7  2  8  3  9  4 10

There are several ways to find out which position each card occupies .
1) index of
   0  6  1  7  2  8  3  9  4 10 i. i.11
0  2  4  6  8 10  1  3  5  7  9
2) grading
   /: 0  6  1  7  2  8  3  9  4 10
0  2  4  6  8 10  1  3  5  7  9
3) and computing the positions with modulo
   11 | 2*i.11
0  2  4  6  8 10  1  3  5  7  9

Going from the positions to the card layout can also be done several ways :
4) assignment
   (i.11) ( 0  2  4  6  8 10  1  3  5  7  9 ) } 11$0
0  6  1  7  2  8  3  9  4 10
5) grading
   /: 0  2  4  6  8 10  1  3  5  7  9
0  6  1  7  2  8  3  9  4 10
6) and, this is the kicker for me, modulo with the right multiplier
   11 | 6*i.11
0  6  1  7  2  8  3  9  4 10

While 3) is obvious, I find 6) disconcerting. And it seems  to work for all
cases where the number of cards and the interval between cards are coprime.

I know this must be explained somewhere but I can't find the relevant
material.

Thanks for your assistance,

Jimmy