#17560: Implement (quantum) Mobius algebras
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.9
Component: combinatorics | Resolution:
Keywords: posets, mobius | Merged in:
algebra | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 4e51ab0a00e0784de44d7da40f92dc078c48f440
public/combinat/mobius_algebras-17560| Stopgaps:
Dependencies: |
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Comment (by tscrim):
Replying to [comment:8 kdilks]:
> * E and C bases for quantum mobius algebras just say that they're bases
for mobius algebras in the docstring (KL does specify quantum mobius
algebra).
Fixed.
> * Throw in the word 'principal' when referring to {{{I_x}}} and
{{{F^x}}} being the order ideal and filter associated to x, just to make
it clear.
Fixed.
> * I think the assumptions related to {{{kazhdan_lusztig_polynomial()}}}
need to be cleaned up some. The docstring says it's defined for a graded,
bounded poset. The paper makes me think it should only be defined for
geometric lattices (ie, corresponding to a matroid). And the code only
checks to see if the poset is ranked.
If you go through their definitions, you find you just need these
conditions (I confirmed this from the authors). I only need to check the
ranked (graded) conditions because the finiteness guarantees bounded.
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Ticket URL: <http://trac.sagemath.org/ticket/17560#comment:10>
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