#14981: Descent algebra
---------------------------------------------+-----------------------------
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:
---------------------------------------------+-----------------------------
Comment (by darij):
Hi Travis,
thanks for looking into this (and spotting the hyphens).
I still think the unity does not belong to the I basis, and your tests are
wrong because your B-to-I and I-to-B transform methods handle the case of
[n] in a special (and incorrect) way. Theorem 3.4 of the Garsia-Reutenauer
paper, applied to r = [n], says that B_{[n]} is a linear combination (with
nonzero coefficients) of all the I_q for q \leq_{\pi} [n] (and that means
for all compositions q of n). In particular, B_{[n]} (which is the 1) is
not a single basis element unless n \leq 1.
Care to add an empty-set check in the doctest of {{{__getitem__}}}? I
think it would be better to explain this nonstandard syntax ({{{D[3,4]}}}
instead of {{{D([3,4])}}}) in a more visible docstring, too.
I hate to say this but your patch is still getting rejected due to the
all.py and algebra.rst insertion points. IMHO this is a weakness of hg (or
the way we are using it), since it shouldn't actually matter where things
are inserted in these two files; but for now, in order maybe you could
move your insertions into some place where there has been no conflicting
patch activity lately? Sorry for this stupid issue.
Best regards,
Darij
--
Ticket URL: <http://trac.sagemath.org/ticket/14981#comment:5>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
