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Dec
8
 awarded  Scholar
Dec
8
 accepted Do these special power functions generate all homogeneous symmetric polynomials?
Dec
8
 comment Do these special power functions generate all homogeneous symmetric polynomials?
Never mind, got it.
Dec
8
 comment Do these special power functions generate all homogeneous symmetric polynomials?
@Marc van Leeuwen: I just meant as a formal linear combination over the rational numbers.
Dec
8
 revised Do these special power functions generate all homogeneous symmetric polynomials?
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Dec
8
 comment Do these special power functions generate all homogeneous symmetric polynomials?
Thanks, I meant to say homogeneous of a given degree.
Dec
8
 comment Do these special power functions generate all homogeneous symmetric polynomials?
Thanks, Greg for the answer and examples. Actually, I was interested in the product (in this case, $xyzw$) and worked that out for a few cases and thought this might work in general. Is there an argument that will work in general for products of variables when $n>4$?
Dec
8
 awarded  Student
Dec
8
 awarded  Editor
Dec
8
 revised Do these special power functions generate all homogeneous symmetric polynomials?
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Dec
8
 asked Do these special power functions generate all homogeneous symmetric polynomials?