#11122: Implementation of the Demazure product in Coxeter groups
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Reporter: stumpc5 | Owner:
Type: enhancement | Status: closed
Priority: major | Milestone:
sage-duplicate/invalid/wontfix
Component: combinatorics | Resolution:
duplicate
Keywords: Demazure product, subword complex | Work issues:
Report Upstream: N/A | Reviewers:
Christian Stump
Authors: | Merged in:
Dependencies: | Stopgaps:
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Changes (by jdemeyer):
* status: positive_review => closed
* reviewer: mshimo => Christian Stump
* resolution: => duplicate
* author: Christian Stump =>
Old description:
> The provided patch implements the Demazure product of a word in the
> generators of a Coxeter group.
>
> The definition can be found e.g. in "Knutson, Miller - Subword complexes
> for Coxeter groups".
>
> {{{
>
> sage: W = CoxeterGroup(['A',2],index_set=[1,2])
>
> sage: w = W.demazure_product([2,2,1])
> sage: w.reduced_word()
> word: 21
>
> sage: w = W.demazure_product([2,1,2,1,2])
> sage: w.reduced_word()
> word: 121
>
> sage: W = CoxeterGroup(['B',2],index_set=[1,2])
>
> sage: w = W.demazure_product([2,1,2,1,2])
> sage: w.reduced_word()
> word: 2121
> }}}
>
> As I also needed it, the patch provides in addition a method returning
> the cartan type of a Coxeter group.
>
> Depends on Ticket #8359.
New description:
The provided patch implements the Demazure product of a word in the
generators of a Coxeter group.
The definition can be found e.g. in "Knutson, Miller - Subword complexes
for Coxeter groups".
{{{
sage: W = CoxeterGroup(['A',2],index_set=[1,2])
sage: w = W.demazure_product([2,2,1])
sage: w.reduced_word()
word: 21
sage: w = W.demazure_product([2,1,2,1,2])
sage: w.reduced_word()
word: 121
sage: W = CoxeterGroup(['B',2],index_set=[1,2])
sage: w = W.demazure_product([2,1,2,1,2])
sage: w.reduced_word()
word: 2121
}}}
As I also needed it, the patch provides in addition a method returning the
cartan type of a Coxeter group.
Duplicate of #12774.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11122#comment:10>
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