List questions from symmetric-polynomials

Published on 12 Jul 2019 - 7:42

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Coefficients of polynomial $(x+1)(x+2)...(x+n)$

Published on 12 Jul 2019 - 20:55

407

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Let $x, y, z$ be real numbers. If $x + y + z = 1$ and $x^2 + y^2 + z^2 = 1$, then what is the minimum value of $x^3 + y^3 + z^3$?

Published on 14 Jul 2019 - 7:54

191

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Multivariate Polynomial Defined Recursively By A Resultant Function

Published on 23 Feb 2026 - 1:17

272

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$\frac{(x-y)(x-z)}{x^2}+\frac{(y-x)(y-z)}{y^2}+\frac{(z-x)(z-y)}{z^2}\geq 0$

Published on 20 Jul 2019 - 21:27

126

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Product of List of Polynomials in Macaulay2

Published on 22 Mar 2026 - 2:31

471

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It may be a strengthening form of mean inequality

Published on 25 Mar 2026 - 9:27

170

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Polynomial division first!

Published on 08 Aug 2019 - 8:46

227

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Can all 3 vector products $\left(\sum_i v_i u_i w_i\right)$ define linear subspace modulo permutation of coordinates?

Published on 25 Mar 2026 - 17:40

1.1k

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Write a homogeneous polynomial of degree $d$ as a sum of $d$-th power of linear polynomials

Published on 09 Aug 2019 - 6:42

192

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How can I solve prove that $8(1-a)(1-b)(1-c)\le abc$ with the conditions below?

Published on 25 Mar 2026 - 6:12

143

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Monotonicity of quotients of elementary symmetric polynomials

Published on 25 Mar 2026 - 16:03

61

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Inequality with a precondition

Published on 25 Mar 2026 - 9:33

106

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If $a,b \in \mathbb{R}$ and $a+b\ge 0$, prove that $(a^2+b^2)^3\ge 32(a^3+b^3)(ab-a-b)$

Published on 23 Aug 2019 - 16:52

78

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A problem on inequality

Published on 24 Aug 2019 - 18:05

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How to solve simultaneous equations with both of the equations being quadratic equations.

Coefficients of polynomial $(x+1)(x+2)...(x+n)$

Let $x, y, z$ be real numbers. If $x + y + z = 1$ and $x^2 + y^2 + z^2 = 1$, then what is the minimum value of $x^3 + y^3 + z^3$?

Multivariate Polynomial Defined Recursively By A Resultant Function

$\frac{(x-y)(x-z)}{x^2}+\frac{(y-x)(y-z)}{y^2}+\frac{(z-x)(z-y)}{z^2}\geq 0$

Product of List of Polynomials in Macaulay2

It may be a strengthening form of mean inequality

Polynomial division first!

Can all 3 vector products $\left(\sum_i v_i u_i w_i\right)$ define linear subspace modulo permutation of coordinates?

Write a homogeneous polynomial of degree $d$ as a sum of $d$-th power of linear polynomials

How can I solve prove that $8(1-a)(1-b)(1-c)\le abc$ with the conditions below?

Monotonicity of quotients of elementary symmetric polynomials

Inequality with a precondition

If $a,b \in \mathbb{R}$ and $a+b\ge 0$, prove that $(a^2+b^2)^3\ge 32(a^3+b^3)(ab-a-b)$

A problem on inequality

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