#11010: Implementation of the SubwordComplex as defined by Knutson and Miller
-----------------------------+----------------------------------------------
Reporter: stumpc5 | Owner: tbd
Type: enhancement | Status: needs_work
Priority: major | Milestone:
Component: combinatorics | Keywords: subword complex, simplicial
complex
Work_issues: | Upstream: N/A
Reviewer: | Author: Christian Stump
Merged: | Dependencies: 11187, 11122
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Changes (by stumpc5):
* dependencies: => 11187, 11122
Old description:
> This patch provides an implementation of the subword complex:
>
> Fix a Coxeter system (W,S). Let Q = be a finite word in S and pi in W.
>
> The subword complex Delta(Q,pi) is then defined to be the simplicial
> complex with vertices being {0,...,n-1}, (n = len(Q), one vertex for each
> letter in Q) and with facets given by all (indices of) subwords Q' of Q
> for which Q\Q' is a reduced expression for pi.
>
> {{{
> sage: W = CoxeterGroup(['A',2])
> sage: w = W.from_reduced_word([1,2,1])
> sage: C = SubwordComplex([2,1,2,1,2],w); C
> Subword complex of type ['A', 2] for Q = [2, 1, 2, 1, 2] and pi = [1,
> 2, 1]
> sage: C.facets()
> {(1, 2), (3, 4), (0, 4), (2, 3), (0, 1)}
> }}}
>
> Depends on Tickets #8359 and #11122.
New description:
This patch provides an implementation of the subword complex:
Fix a Coxeter system (W,S). Let Q = be a finite word in S and pi in W.
The subword complex Delta(Q,pi) is then defined to be the simplicial
complex with vertices being {0,...,n-1}, (n = len(Q), one vertex for each
letter in Q) and with facets given by all (indices of) subwords Q' of Q
for which Q\Q' is a reduced expression for pi.
{{{
sage: W = CoxeterGroup(['A',2],index_set=[1,2])
sage: w = W.from_reduced_word([1,2,1])
sage: C = SubwordComplex([2,1,2,1,2],w); C
Subword complex of type ['A', 2] for Q = [2, 1, 2, 1, 2] and pi = 121
sage: C.facets()
{(1, 2), (3, 4), (0, 4), (2, 3), (0, 1)}
}}}
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11010#comment:2>
Sage <http://www.sagemath.org>
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