Partition ordering

[franktaw at netscape.net]

There are two methods for ordering partitions of an integer in use in the Encyclopedia - one as defined by Abramowitz and Stegun, and the other as generated by Mathematica.  The problem I have is that I can see three reasonable ways of ordering partitions, and I'm not sure which one Abramowitz and Stegun uses.
 
To me, the most natural way to order the partitions is lexicographically - so, for example, the partitions of 9 would start [9], [8,1], [7,2], [7,1,1], [6,3], ....  (Note that this is reversed - the highest numbers come first.) This appears to be the way that Mathematica generates them - see A080577.
 
The second ordering is to order first by size (increasing), and then lexicographically.  This is consistent with what I can see of the the A&S ordering - see A036037.
 
The third ordering is a reverse lexicographic ordering - to compare two partitions, look not for the first difference (as for lexicographic ordering) but for the last one, and compare those.  (We consider the partitions to be padded with zeros for this purpose, so [2,2], padded to [2,2,0] comes before [2,1,1].)  This ordering is also compatible with what I can see of A&S.  (Note that this ordering automatically sorts shorter partitions before longer ones.)
 
So my question is, which ordering does A&S use?  The first difference between my second and third orderings is for n=9, where the second ordering puts [5,2,2] before [4,4,1], while the third reverses them.
 
Franklin T. Adams-Watters
16 W. Michigan Ave.
Palatine, IL 60067
847-776-7645
___________________________________________________
Try the New Netscape Mail Today!
Virtually Spam-Free | More Storage | Import Your Contact List
http://mail.netscape.com
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://list.seqfan.eu/pipermail/seqfan/attachments/20060111/5f50e637/attachment.htm>