List questions from symmetric-polynomials

Published on 16 Apr 2020 - 5:01

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Inequality with 4 variables

Published on 25 Mar 2026 - 12:52

71

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For $a,b,c\ge0$, show $a^2 + b^2 + c^2 = 3$ implies $(a^3 + b^3 + c^3)^2 \geq 3 + 2(a^4 + b^4 + c^4)$.

Published on 25 Mar 2026 - 12:41

113

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Expansion of $(x+y)^n+(x+z)^n+(y+z)^n-x^n-y^n-z^n$ in terms of elementary symmetric polynomials

Published on 25 Mar 2026 - 17:44

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Symmetric polynomials; $a_1,a_2,\ldots,a_n\in\Bbb{C}$ s.t. $\prod_{i=0}^n\left(a_i^k+1\right)=1,\;\forall k\in\Bbb{N}\implies a_1=\dots =a_n=0$

Published on 19 Apr 2020 - 16:03

114

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Are there simple expressions for skew Schur polynomials corresponding to hook-shaped diagrams?

Published on 22 Apr 2020 - 14:37

87

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Prove that $3x^3-41x+48\leq 0$ for $x \in [\sqrt 3, \sqrt 6]$

Published on 23 Apr 2020 - 12:11

23

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What role do symmetries play in solving a quadratic and higher degree polynomial?

Published on 23 Apr 2020 - 21:25

70

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How to analyze the equation $(x-y)^2=2\big( (x+y)-2\sqrt{xy} \big)$?

Published on 26 Mar 2026 - 11:18

30

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A Problem on Symmetric Polynomials.

Published on 26 Apr 2020 - 13:14

524

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Lagrange Method of Solving Cubic Equations

Published on 26 Mar 2026 - 22:19

342

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Prove that for all positives $a, b$ and $c$, $(\sum_{cyc}\frac{c + a}{b})^2 \ge 4(\sum_{cyc}ca)(\sum_{cyc}\frac{1}{b^2})$.

Published on 25 Mar 2026 - 9:28

74

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Stuck when transforming and solving this

Published on 25 Mar 2026 - 9:33

139

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Prove $\Big[\sum\limits_{cyc} a(a^2+2bc)\Big]^3 \geqq 3(ab+bc+ca)^2 . \sum\limits_{cyc} a(a^2+2bc)^2$

Published on 25 Mar 2026 - 9:40

163

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A certain composition into the elementary symmetric polynomials

Published on 25 Mar 2026 - 22:30

List Question

Factorising an anti-symmetric polynomial

Inequality with 4 variables

For $a,b,c\ge0$, show $a^2 + b^2 + c^2 = 3$ implies $(a^3 + b^3 + c^3)^2 \geq 3 + 2(a^4 + b^4 + c^4)$.

Expansion of $(x+y)^n+(x+z)^n+(y+z)^n-x^n-y^n-z^n$ in terms of elementary symmetric polynomials

Symmetric polynomials; $a_1,a_2,\ldots,a_n\in\Bbb{C}$ s.t. $\prod_{i=0}^n\left(a_i^k+1\right)=1,\;\forall k\in\Bbb{N}\implies a_1=\dots =a_n=0$

Are there simple expressions for skew Schur polynomials corresponding to hook-shaped diagrams?

Prove that $3x^3-41x+48\leq 0$ for $x \in [\sqrt 3, \sqrt 6]$

What role do symmetries play in solving a quadratic and higher degree polynomial?

How to analyze the equation $(x-y)^2=2\big( (x+y)-2\sqrt{xy} \big)$?

A Problem on Symmetric Polynomials.

Lagrange Method of Solving Cubic Equations

Prove that for all positives $a, b$ and $c$, $(\sum_{cyc}\frac{c + a}{b})^2 \ge 4(\sum_{cyc}ca)(\sum_{cyc}\frac{1}{b^2})$.

Stuck when transforming and solving this

Prove $\Big[\sum\limits_{cyc} a(a^2+2bc)\Big]^3 \geqq 3(ab+bc+ca)^2 . \sum\limits_{cyc} a(a^2+2bc)^2$

A certain composition into the elementary symmetric polynomials

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