#10305: Add rings for the center of the symmetric group algebras
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Reporter: mguaypaq | Owner:
mguaypaq
Type: enhancement | Status:
needs_work
Priority: minor | Milestone:
sage-5.8
Component: combinatorics | Resolution:
Keywords: combinatorics, rings, symmetric functions | Work issues:
Report Upstream: N/A | Reviewers:
Authors: Mathieu Guay-Paquet | Merged in:
Dependencies: | Stopgaps:
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Comment (by tscrim):
Hey Mathieu,
Replying to [comment:4 mguaypaq]:
> It's been a while, but my recollection is that the code works most of
the time, but several doctests are missing before it's acceptable. Also
the performance is not great.
I'd be happy to write a review patch and add in the documentation.
> To fix the problems with the code (mostly some coercions and performance
issues), I think a better architecture would be needed. In particular, not
using {{{CombinatorialFreeModule}}} would probably be better. We also have
a better understanding of the mathematics behind the various changes of
basis between symmetric functions and the Farahat-Higman algebra now, and
this could be used for the code. I tried doing this a few times, but never
got to the end.
There has also be a very substantial rewrite of the symmetric functions
and we would likely be able to lift some code (or at least the
implementation concepts) from there.
> Do you have a need for this functionality? If so, I'd be happy to
collaborate or let you take over. Otherwise, I think this ticket can be
safely ignored and/or closed for now.
It would be nice for a colleague of mine to have a working version of this
in sage. Right now he's looking into Schur rings in Z(CC[S_n]) as they
come up in supercharacter theory and this patch would be useful. I'm happy
to help where I can to get this working.
Best,[[BR]]
Travis
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10305#comment:5>
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