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<DIV><FONT face=Arial size=2><SPAN class=305084614-17062007>Dear Seqfans
-</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN
class=305084614-17062007></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=305084614-17062007>Suppose p is a
permutation of the positive integers, N. If we subtract 1 from every term
and then delete 0, what's left is another perm. Iterate, and we get many
perms.</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN
class=305084614-17062007></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=305084614-17062007>Now, let t(k) be the
position of 1 in the kth iterate.</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN
class=305084614-17062007></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=305084614-17062007>Example: p =
(1,3,2,5,7,4,9,11,6,13,15,8,...) = A006369 (related to 3X+1
problem)</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN class=305084614-17062007>This choice of p
yields trace sequence t = (1,2,1,3,1,4,1,5,1,6,1,7,...) = A057979
essentially.</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN
class=305084614-17062007></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=305084614-17062007>A sequence t of
positive integers is the trace of a perm if and only if t has infinitely
many 1's. Let T be the set of all such t.</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN
class=305084614-17062007></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=305084614-17062007>Suppose t_p and t_q
are traces of perms p and q. Can someone find a decent formula for t_r,
where r is the composite perm p-of-q?</SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN
class=305084614-17062007></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=305084614-17062007>I'd like to see such
a formula - it would define a group operation on the set
T. </SPAN></FONT></DIV>
<DIV><FONT face=Arial size=2><SPAN
class=305084614-17062007></SPAN></FONT> </DIV>
<DIV><FONT face=Arial size=2><SPAN class=305084614-17062007>Clark
Kimberling
</SPAN></FONT></DIV></BODY></HTML>