Maple partition ordering

[Jaap Spies]

franktaw at netscape.net wrote:
> Looking at A080576, it appears that the Maple partition ordering is just the reverse of the Mathematica ordering.  That is, the partitions of n are sorted by the largest element in increasing order, then by the second largest, etc.  (Where the Mathematica ordering sorts by largest element in decreasing order, etc.)  However, the values in the OEIS do not go high enough to be sure.
>  
> Can someone with access to Maple please verify this?  You need check at least n=9.
>  


 > seq(partition(n),n=1..10);

[[1, 1], [2]],

  [[1, 1, 1], [1, 2], [3]],

   [[1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3], [4]],

   [[1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], [1, 1, 3], [2, 3], [1, 4], 
[5]],

   [[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 2], [1, 1, 2, 2], [2, 2, 2], [1, 1, 
1, 3],

   [1, 2, 3], [3, 3], [1, 1, 4], [2, 4], [1, 5],

   [6]],

   [[1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 2], [1, 1, 1, 2, 2], [1, 2, 
2, 2],

   [1, 1, 1, 1, 3], [1, 1, 2, 3], [2, 2, 3], [1, 3, 3], [1, 1, 1, 4],

   [1, 2, 4], [3, 4], [1, 1, 5], [2, 5], [1, 6],

   [7]],

   [[1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 2, 2],

   [1, 1, 2, 2, 2], [2, 2, 2, 2], [1, 1, 1, 1, 1, 3], [1, 1, 1, 2, 3],

   [1, 2, 2, 3], [1, 1, 3, 3], [2, 3, 3], [1, 1, 1, 1, 4], [1, 1, 2, 4],

   [2, 2, 4], [1, 3, 4], [4, 4], [1, 1, 1, 5], [1, 2, 5], [3, 5], [1, 1, 6],

   [2, 6], [1, 7],

   [8]],

   [[1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 2],

   [1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 2, 2, 2], [1, 2, 2, 2, 2],

   [1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 2, 3], [1, 1, 2, 2, 3], [2, 2, 2, 3],

   [1, 1, 1, 3, 3], [1, 2, 3, 3], [3, 3, 3], [1, 1, 1, 1, 1, 4],

   [1, 1, 1, 2, 4], [1, 2, 2, 4], [1, 1, 3, 4], [2, 3, 4], [1, 4, 4],

   [1, 1, 1, 1, 5], [1, 1, 2, 5], [2, 2, 5], [1, 3, 5], [4, 5], [1, 1, 
1, 6],

   [1, 2, 6], [3, 6], [1, 1, 7], [2, 7], [1, 8],

   [9]],

   [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1, 1, 2],

   [1, 1, 1, 1, 1, 1, 2, 2], [1, 1, 1, 1, 2, 2, 2], [1, 1, 2, 2, 2, 2],

   [2, 2, 2, 2, 2], [1, 1, 1, 1, 1, 1, 1, 3], [1, 1, 1, 1, 1, 2, 3],

   [1, 1, 1, 2, 2, 3], [1, 2, 2, 2, 3], [1, 1, 1, 1, 3, 3], [1, 1, 2, 3, 3],

   [2, 2, 3, 3], [1, 3, 3, 3], [1, 1, 1, 1, 1, 1, 4], [1, 1, 1, 1, 2, 4],

   [1, 1, 2, 2, 4], [2, 2, 2, 4], [1, 1, 1, 3, 4], [1, 2, 3, 4], [3, 3, 4],

   [1, 1, 4, 4], [2, 4, 4], [1, 1, 1, 1, 1, 5], [1, 1, 1, 2, 5], [1, 2, 
2, 5],

   [1, 1, 3, 5], [2, 3, 5], [1, 4, 5], [5, 5], [1, 1, 1, 1, 6], [1, 1, 
2, 6],

   [2, 2, 6], [1, 3, 6], [4, 6], [1, 1, 1, 7], [1, 2, 7], [3, 7], [1, 1, 8],

   [2, 8], [1, 9],

   [10]]


Regards,

Jaap