#18050: Implement dual equivalence graphs
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.6
Component: combinatorics | Resolution:
Keywords: dual equivalence | Merged in:
graphs | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 65ddba1c9e657a5315b815418d6d336acb07caff
public/crystals/dual_equivalence-18050| Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Comment (by tscrim):
Replying to [comment:17 darij]:
> I've been through (the easy) part of the code. Nice to see this going
into Sage!
Thanks for doing the review.
> My question is still standing: Where are the `= 0 or 1` conditions in
Assaf's (4.1) reflected in your code and doc? Or are they redundant, or
wrong, or your notion of dual equivalence graphs different?
It's in the code, see this line:
{{{
if x.epsilon(i) == 1 and x.epsilon(im) == 0:
}}}
Note that because I considered the directed, I make it slightly more
specific than Assaf's definition by saying `\varepsilon_j(b) = 1`. A
similar statement appears in the doc.
> Also, I had to change the meaning of "head" (of a directed edge) in the
partitions.py method; please check whether it is correctly used in the
other file.
It looks okay. I think instead of writing `a - b` we should do `a \to b`
in both files for directed edges (especially since it's in latex).
I also feel this statement is too verbose:
{{{
- In the one-line notation of the permutation `p`, the letter
`i` appears either to the left of both `i-1` and `i+1`, or
to the right of both `i-1` and `i+1` (but not between the
two).
}}}
and we should just say `i` does not appear between `i-1` and `i+1`. Does
this sound okay?
> In regular_crystals.py, what is required of X ? Should it be closed
under e_i and f_i?
No, I wanted it to be as general as possible (at least this is what I
needed for my research; I didn't necessarily know if my set of elements
was the full dual equivalence class).
--
Ticket URL: <http://trac.sagemath.org/ticket/18050#comment:18>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
