#18050: Implement dual equivalence graphs
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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: | 274a0187d4382d8fd24bf6a72f0b54bb5a64b580
public/crystals/dual_equivalence-18050| Stopgaps:
Dependencies: |
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Comment (by tscrim):
Replying to [comment:13 darij]:
> Oh. Is `\delta_j(b)` the same as your `-\varphi_j(b)`?
Yes.
> And what does the `= 0 or 1` part of Assaf's (4.1) correspond to in your
definition?
It means that we can do the `e_i` operation exactly 0 or 1 times before it
falls off the crystal graph. In other words, these conditions state that
if there is an `i`-arrow in the crystal graph going through `b`, then the
entire chain of `i`-arrows containing `b` has length 2 with `b` in the
middle.
@mantepse I will make those changes in a minute.
--
Ticket URL: <http://trac.sagemath.org/ticket/18050#comment:14>
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