List questions from symmetric-polynomials

Published on 05 Aug 2018 - 6:21

118

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Find maximal permutation group $G$ such that a polynomial is $G$-invariant

Published on 05 Aug 2018 - 6:48

504

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symmetric polynomial recursion to solve the system, $x^5+y^5=33$, $x+y=3$

Published on 06 Aug 2018 - 1:01

106

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If $a$, $b$ and $c$ are positive then $\sum\limits_{cyc} \frac{a^{2}}{b^{2}+c^{2}+bc}\geq 1$

Published on 20 Mar 2026 - 5:20

154

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Prove that: $\sum\limits_{cyc} \frac{b+c}{a^{2}+bc}\leq \sum\limits_{cyc} \frac{1}{a}$

Published on 07 Aug 2018 - 5:18

200

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Prove that: $\frac{bc}{a^2+1}+\frac{ac}{b^2+1}+\frac{ab}{c^2+1}\leq \frac{3}{4}$

Published on 07 Aug 2018 - 16:59

667

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Symmetric polynomial identities: $(x,y,z)^n$ in terms of $\sigma _1=x+y+z$, $\sigma _2 = xy+yz+xz$ and $\sigma _3 = xyz$

Published on 25 Mar 2026 - 3:04

136

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Can the "symmetric algebra" over $\mathbb R^n$ be defined from an infinite-dimensional exterior algebra?

Published on 25 Mar 2026 - 5:07

181

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How to prove AM-GM by induction 3

Published on 10 Aug 2018 - 17:57

113

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Inequality about Schur

Published on 12 Aug 2018 - 13:51

71

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Find solution following the system of equations!

Published on 12 Aug 2018 - 15:42

347

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find minimum value of $n$ that satisfies this inequality: $4(x_1^2+x_2^2+...+x_n^2)<2(x_1+x_2+...+x_n)<x_1^3+x_2^3+...+x_n^3$

Published on 17 Aug 2018 - 9:16

568

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Inequality $\sqrt{xy+yz+zx} \ge \frac {8}{15} (x+y+z)$

Published on 17 Aug 2018 - 12:36

172

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Analogues of the elementary symmetric polynomials for the alternating group

Published on 19 Aug 2018 - 17:24

226

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If $x+y+z=3$ then $\sum x\sqrt{x^3+3y} \ge 6$

Published on 25 Mar 2026 - 6:06

List Question

inequality involving $(xy+yz+zx)^3$ and the $pqr$ method

Find maximal permutation group $G$ such that a polynomial is $G$-invariant

symmetric polynomial recursion to solve the system, $x^5+y^5=33$, $x+y=3$

If $a$, $b$ and $c$ are positive then $\sum\limits_{cyc} \frac{a^{2}}{b^{2}+c^{2}+bc}\geq 1$

Prove that: $\sum\limits_{cyc} \frac{b+c}{a^{2}+bc}\leq \sum\limits_{cyc} \frac{1}{a}$

Prove that: $\frac{bc}{a^2+1}+\frac{ac}{b^2+1}+\frac{ab}{c^2+1}\leq \frac{3}{4}$

Symmetric polynomial identities: $(x,y,z)^n$ in terms of $\sigma _1=x+y+z$, $\sigma _2 = xy+yz+xz$ and $\sigma _3 = xyz$

Can the "symmetric algebra" over $\mathbb R^n$ be defined from an infinite-dimensional exterior algebra?

How to prove AM-GM by induction 3

Inequality about Schur

Find solution following the system of equations!

find minimum value of $n$ that satisfies this inequality: $4(x_1^2+x_2^2+...+x_n^2)<2(x_1+x_2+...+x_n)<x_1^3+x_2^3+...+x_n^3$

Inequality $\sqrt{xy+yz+zx} \ge \frac {8}{15} (x+y+z)$

Analogues of the elementary symmetric polynomials for the alternating group

If $x+y+z=3$ then $\sum x\sqrt{x^3+3y} \ge 6$

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