#14981: Descent algebra
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Reporter: tscrim | Owner: sage-
Type: enhancement | combinat
Priority: major | Status: needs_review
Component: combinatorics | Milestone: sage-5.12
Keywords: Solomon's descent algebra | Resolution:
Authors: Travis Scrimshaw | Merged in:
Report Upstream: N/A | Reviewers:
Branch: | Work issues:
Stopgaps: | Dependencies:
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Old description:
> Implement Solomon's descent algebra (for type A,,n-1,,) with the bases D
> (descents), B (subsets), and I (idempotents) following Garsia and
> Reutenauer.
New description:
Implement Solomon's descent algebra (for type A,,n-1,,) with the bases D
(descents), B (subsets), and I (idempotents) following Garsia and
Reutenauer.
----
Apply: [attachment:trac_14981-descent_algebra-ts.patch]
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Comment (by tscrim):
Hey Darij,
Here's a new version of the patch with your first review patch folded in.
I've fixed the above issue with some input checks and added coercions into
NSym and the sym. gp. algebra (which should be okay since it's getting
permutations via descents). In the I basis, it is also indexed by
compositions, so I,,[n],, is a basis element and is 1:
{{{
sage: I = DescentAlgebra(QQ, 5).I()
sage: for b in I.basis():
....: if I.one() * b != b * I.one():
....: print b
....:
sage: I.one() * I.one() == I.one()
True
}}}
Thanks for also filling out the references.
Ready for continued review.
Thanks,[[BR]]
Travis
PS - Be careful with hyphens when copy/pasting since often times they
aren't ascii.
For patchbot:
Apply: trac_14981-descent_algebra-ts.patch
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Ticket URL: <http://trac.sagemath.org/ticket/14981#comment:4>
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