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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
