Relationship between disorder of a permutation and order of a permutation Is there any relationship between disorder of a permutation and order of a permutation?
 A: Emeric Deutsch said at OEIS A008302

The disorder of a permutation $p$ of
  $(1,2,\ldots ,n)$ is defined in the
  following manner. We scan $p$ from left
  to right as often as necessary until
  all its elements are removed in
  increasing order, scoring one point
  for each occasion on which an element
  is passed over and not removed. The
  disorder of $p$ is the number of points
  scored by the end of the scanning and
  removal process. For example, the
  disorder of $(3,5,2,1,4)$ is $8$, since on
  the first scan, $3$, $5$, $2$ and $4$ are passed
  over, on the second, $3$, $5$ and $4$ and on
  the third scan, $5$ is once again not
  removed.

That suggests that the disorder is calculated from the order. Is that what you are looking for?
A: I've defined the disorder in my comment on Henry's answer. (EDIT: this is the way it is defined in Section 2.13 of Chris Cooper's notes.) If the disorder is zero then $p$ is the identity, order $1$. If the disorder is $1$ then $p$ is a transposition, in fact, a transposition of the form $(a\quad a+1)$, so of order $2$. But if the disorder is $2$ then $p$ could be $(a\quad a+1)(b\quad b+1)$ of order $2$ or $(a\quad a+1\quad a+2)$ of order $3$. The disorder can be high even if the order is $2$ (use $(1\quad n)$), and fairly low even if the order is high (e.g. $(1\quad2)(3\quad4\quad5)(6\quad7\quad8\quad9\quad10)$ has disorder $7$ and order $30$). In short, I don't think you can say very much about either number based solely on knowledge of the other. 
