'Mixing number' of permutations

[Rob Pratt]

Seems related to "connected permutations":
http://www.research.att.com/~njas/sequences/A003319 

-----Original Message-----
From: Hugo Pfoertner [mailto:all at abouthugo.de] 
Sent: Thursday, August 17, 2006 8:30 AM
To: seqfan at ext.jussieu.fr; fc3a501 at uni-hamburg.de
Subject: 'Mixing number' of permutations

SeqFans,

today Hauke Reddmann started a new thread in the NG sci.math

http://groups.google.com/group/sci.math/msg/b1c1164b936c6dca

<<
For easyness, I use the data of my lest chess tournament :-) The finish in terms of the starting numbers was
7 1 6 4 3 8 5 2|9|10|14 15 20 13 18 16 23 22 12 26 11 17 19 27 25 21
24|28

A | marks boundaries between consecutive number subsets that permute to themselves. Note that I (the 16) also permute to myself, but there are number crossing from both sides and so this is no boundary.

Obvious question: How many boundaries occur in a random permutation?
Clearly a tournament is about the opposite of random, as the swap numbers will be low.

Example n=3

1|2|3
1|3 2
2 1|3
2 3 1
3 1 2
3 2 1
-- 
Hauke Reddmann <:-EX8    fc3a501 at uni-hamburg.de
His-Ala-Sec-Lys-Glu Arg-Glu-Asp-Asp-Met-Ala-Asn-Asn
>>

Is there anything in the OEIS that can answer his question? Any other ideas?

Can you please CC answers also to Hauke; AFAIK he is not member of the Seqfan community.

Hugo Pfoertner