[seqfan] Re: Please help to check A074140.

[Peter Luschny]

http://oeis.org/wiki/Orderings_of_partitions#A%20comparison
There I read:

"This is the alternative (non-reflected) "Abramowitz and Stegun" ordering
of the partitions, referenced in numerous (?) other sequences. The
alternative (non-reflected) "Abramowitz and Stegun" ordering of the
partitions (parts in decreasing order) is the graded colexicographic
ordering of the partitions. The partitions are in reverse order of the
conjugates of the partitions in "Mathematica" order (A080577). Each
partition is the conjugate of the corresponding partition in "Maple" order."

I have a hard time to understand this. I would like to have a
*context-free* definition of all this stuff, not a heap of terms
pointing to one another. The very position of the term 'reverse'
in these descriptions often makes several readings possible.

It would be very helpful to see algorithms which describe the
meaning of all these terms in a precise, unique way.

Peter