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Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
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About Turan`s problem(inequality) in multivariable
I am sorry. Ottem is right. $P_n$ is a polynomial of degree $n$. In particular, you may assume that $P_n$ is a symmetric function. Let's focus that $P_n(x_1,\, \dots ,x_k) = x_1^n + \cdots + x_k^n$, f …