Dan Asimov <dasimov@earthlink.net> wrote:

Does the circular character string have marked "ends", or merely a circular ordering?

That depends on what you mean by ends. I consider it to have a specific beginning and end. I regard a rotation of a string to be different from the original. But the scrambling process ignores the ends, i.e. the scramble of a rotation will be the rotation of the scramble: reverse -> erersev everser -> rerseve versere -> ersever

Is it assigned a direction (orientation)?

Yes. Otherwise the approved term would be bracelet, not necklace.

It seems that the reversals are performed consecutively. Does it matter what order they're performed in? If so, what order should they be performed in?

In the lexical order of delimiters, i.e. ASCII order if we're talking about ASCII strings. Or are you asking about the multiple reversals with each specific delimiter? The order there is irrelevant, since no reversal bridges a delimiter character. For instance when the delimiter is the space bar, this line turns into: tni ecnatsni nehw eht retimiled si eht ecaps ,rab siht enil snrut roF:o regardless of the order of the reversals. (Note that the delimiters don't move.) The next delimiter is the comma, and you get he when instance into:For turns line this bar, space the is delimiter t James Propp <jamespropp@gmail.com> wrote:

14 is divisible by 7 and 16320 is divisible by 40.

Could it be that the size of each orbit is always divisible by the length of the string?

No. For instance if every character is the same, it repeats after 1. If every character is different, it repeats after 1 or 2 depending on whether the number of characters is even or odd. If there are only two distinct characters (e.g. the string is all ones and zeros), it repeats after 1. My main question is really whether this is a known transform, and if so what is it called and where can I learn more about it? Thanks.