#15408: corrections and improvements to `inner_plethysm` method in symmetric
functions
-------------------------------------+-------------------------------------
Reporter: zabrocki | Owner:
Type: defect | Status: needs_review
Priority: major | Milestone: sage-6.0
Component: combinatorics | Resolution:
Keywords: symmertic | Merged in:
functions, inner plethysm | Reviewers:
Authors: Mike Zabrocki | Work issues:
Report Upstream: N/A | Commit:
Branch: | cd4470b77781bdc17787a44d86b948d2c8ff0c75
public/combinat/15408/zabrocki/inner_plethysm| Stopgaps:
Dependencies: |
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Comment (by zabrocki):
Darij, my example of when the statement is when `g` and `h` are of the
same degree, so my edits are only to try to make the doc string clearer.
One of the reasons that I changed it was because I don't understand the
meaning of the sentence "`f.inner_plethysm(g)` is a polynomial in the
coefficients of `g`" It should be a symmetric function, not a polynomial.
The other phrase that appears throughout the docstring is "determine its
values." Unfortunately I don't understand what is meany by the
''values'' of a symmetric function. My modifications of the docstring
avoid this phrase because I don't understand what is intended by that
phrase.
I also think that there is something wrong in the sentence
{{{
we can think of the function `g` as the character of a representation of
the
general linear group, and hence (by Schur-Weyl duality) as the character
of
a representation `\rho` of the symmetric group `S_n`.
}}}
To my eye, `g` would not be a character of an S_n representation, but it
would be a generating
function for the character (Frobenius image of the character). This is
not a serious problem since the object of interest is the representation
`\rho`, but I find the use of Schur-Weyl duality an unnecessary
complication in the explanation.
Please read the docstring that I wrote. Is it clearer? Can you improve
it more?
--
Ticket URL: <http://trac.sagemath.org/ticket/15408#comment:4>
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