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Answer by user "VA" to question http://mathoverflow.net/questions/14613 :
"This is just to add 1% to Dmitri's 99% complete answer. Change the coordinates to $w_0,\dots, w_{n-1}$ defined by the formula
$$ w_i = x_0 + \mu^i x_1 + \mu^{2i} x_2 + \dots, $$
where $\mu$ is a primitive $n$-th root of identity. Then the ring of invariants is the subring of monomials
$$ w_0^{k_0}\dots w_{n-1}^{k_{n-1}} \quad \text{such that}\quad n\ |\ k_1 + 2k_2 + \dots (n-1) k_n$$
and a set of generators can be obtained by taking minimal such monomials (i.e. not divisible by smaller such monomials). And relations between these generators are of the form (monomial in $w_i$) = (another monomial in $w_i$). That's a pretty easy presentation by any standard.
P.S. This works over $\mathbb C$ or any ring containing $1/n$ and $\mu$."
Notice that this answer, while not adding any new ideas, noticeably improves upon the exposition of Dmitri's one. It is voted +3, so I am surprised the author was able to delete it in the first place...
Only regarding the final comment: Since there is a badge [disciplined] for deleting a post with at least +3 the fact that it was possible to delete it does not seem so suprising to me. (AFAIK only accepted answers, and questions with good [in the sense of score] answers are problematic to delete.)
You cannot delete your own posts in the following cases:
This is my experience from SE 2.0, but I believe that this feature is shared with MO and its obsolete software.
There is an old story here and I think this answer was deleted as part of it. You might be able to figure things out if you check meta threads around the end of April 2010. I don't think anybody would mind if it got undeleted.
Ah, I see! Voting to undelete then, and if possible to scan through the other deleted posts from the same author.
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