#19594: Implement the cactus group
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.0
Component: group theory | Resolution:
Keywords: cactus | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/groups/cactus_group-19594 | 7eb2a1278ea0ca08375f87e0f82081218a2ea1ec
Dependencies: | Stopgaps:
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Comment (by tscrim):
Replying to [comment:13 darij]:
> After a few experiments (on paper), I have started suspecting that
Travis's code *does* bring every word to a normal form. This could be a
cool combinatorial result, if true.
>
> If true, it should be provable using the diamond lemma... Does anyone
volunteer to bash the cases?
I am pretty sure that the terminating condition is possible, but I'm
worried about a case of something like `s[4, 5] * s[1, 7] * s[5, 8]` and
the shuffles. However, I agree it would be a nice little result if this
was true, and as far as I can find, there is no such analogous result. At
the very least, I think we can easily show an analog of Matsumoto's lemma,
and so we build out a reduced word graph and find a lex min element in
that.
--
Ticket URL: <http://trac.sagemath.org/ticket/19594#comment:15>
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