Hey Andrew,
> I will do "reverse lex" (lex order read from right to left) and "reverse
>> dominance" (which I presume is partial sums from right to left). However
>> what is reverse containment?
>>
>
> AH, I guess that "reverse lexicographic" is ambiguous as it could mean
> either reading the words in the reverse order or simply reversing the
> partial order.
>
> For me, and what I meant with all of these orderings, is simply taking the
> same order but in the reverse order:
> x \le_{rev} y <==> y \le x
> Of course, this is a very trivial difference but it is still a significant
> one in terms of the poset and the order in which the partitions are
> generated. In my work, the "reverse" orderings in this sense play a very
> important role: they reflect contragredient duality and also the duality
> arising from tensoring with the sign representations.
>
Ah I see. I will implement a (naive) __reversed__() method for the
partitions (see http://docs.python.org/2/library/functions.html#reversed)
since we've removed __len__() from the partition parents. That way you can
just call `reversed(Partitions(5))` to iterate through in reverse. Expect
it on the next #13605 push.
>
> I have never seen an application of the "right to left" lexicographic
> ordering, although I have this vague feeling that it appears in Stanley's
> book (but then, so do most things!:).
>
I've seen it, although it was in the context of simplicial complexes.
> I don't remember ever seeing the right to left dominance order...
>
I might have just made that up...
Best,
Travis
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