/:p is the inverse permutation for any permutation p . Since /:x and \:x are both permutations it stands to reason that /: computes the inverse. Of course, /:/:x is not necessarily equal to /:\:x (in fact, if p and q are permutations and (/:p)=/:q, then p=q).
The inverse permutation is unique (and the set of all permutations of order n form a group). That is, if p is a permutation and q and r are inverse of p, then q=r . ----- Original Message ----- From: bill lam <[EMAIL PROTECTED]> Date: Monday, September 10, 2007 6:49 Subject: Re: [Jprogramming] inverse permutation vector To: Programming forum <[email protected]> > On further testing, I found that /:pv is the inverse permutation > for both grade > up and grade down, > pv=. /:p and pv=. \:p > > Is the inverse permutation stable for both cases, grade-up and > grade-down? > > > bill lam wrote: > > Raul Miller wrote: > >> ipv=: /: pv > > > > Thank you, I didn't realize that is so simple. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
