#11010: Implementation of the SubwordComplex as defined by Knutson and Miller
-------------------------------------+-------------------------------------
Reporter: stumpc5 | Owner: tbd
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.10
Component: combinatorics | Resolution:
Keywords: subword complex, | Merged in:
simplicial complex | Reviewers:
Authors: Christian Stump | Work issues: coverage
Report Upstream: N/A | Commit:
Branch: u/chapoton/11010 | 046879866540893d9d7f678c2962728a322f0ebd
Dependencies: #12774, #11187 | Stopgaps:
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Comment (by tscrim):
As far as I can see, just one thing is needed:
- `reflections()` (technically `nr_reflections()`, but we can just do
`len(self.reflections())`)
We can construct this easily enough by conjugation of simple reflections:
{{{
sage: W = CoxeterGroup(['A',2])
sage: S = W.simple_reflections()
sage: I = W.index_set()
sage: R = RecursivelyEnumeratedSet(S, lambda x: [S[i]*x*S[i] for i in I if
not x.has_descent(i)], structure="graded")
sage: list(R)
[
[-1 1] [ 1 0] [ 0 -1]
[ 0 1], [ 1 -1], [-1 0]
]
sage: all(x.absolute_length() for x in R)
True
}}}
The `apply_simple_reflection` is already a part of Sage for Coxeter
groups.
Aside - This probably deserves to be in the category of finite Coxeter
groups, but there is some slight conflict with this
{{{
sage: W = WeylGroup(['A',2], prefix='s')
sage: W.reflections()
Finite family {s1*s2*s1: (1, 0, -1), s1: (1, -1, 0), s2: (0, 1, -1)}
}}}
(Trying to do this on the Weyl group on the root system seems to run
forever and `ctrl-C` out results in a nasty error message.)
--
Ticket URL: <http://trac.sagemath.org/ticket/11010#comment:36>
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