Opened 11 years ago

Last modified 9 years ago

#11122 closed enhancement

Implementation of the Demazure product in Coxeter groups — at Initial Version

Reported by: stumpc5 Owned by: tbd
Priority: major Milestone: sage-duplicate/invalid/wontfix
Component: combinatorics Keywords: Demazure product, subword complex
Cc: Merged in:
Authors: Christian Stump Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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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])

            sage: w = W.demazure_product([2,2,1])
            sage: w.reduced_word()
            [2, 1]

            sage: w = W.demazure_product([2,1,2,1,2])
            sage: w.reduced_word()
            [1, 2, 1]

            sage: W = CoxeterGroup(['B',2])

            sage: w = W.demazure_product([2,1,2,1,2])
            sage: w.reduced_word()
            [2, 1, 2, 1]

As I also needed it, the patch provides in addition a method returning the cartan type of a Coxeter group.

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