List questions from symmetric-polynomials

Published on 23 Feb 2026 - 23:33

161

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Order on three real numbers given they are roots of a cubic, their sum and sum of pairwise product

Published on 18 Jul 2021 - 11:44

921

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Prove $a^2 + b^2 + c^2 + ab + bc +ca \ge 6$ given $a+b+c = 3$ for $a,b,c$ non-negative real.

Published on 27 Jul 2021 - 2:25

106

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Hard and non-trivial inequality with three variable reals

Published on 26 Mar 2026 - 19:17

911

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Discriminant of algebraic number field is $0$ or $1 \bmod 4$

Published on 27 Mar 2026 - 0:06

41

Views

Confusion on applying Newton formulae (not Newton's method) technique in finding roots

Published on 06 Aug 2021 - 0:59

75

Views

Interesting inequality with three positive reals which seems trivial

Published on 06 Aug 2021 - 16:13

226

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Prove that $\sum\limits_{cyc}\frac{a^2}{a^2+bc}+\frac{(a+b+c)^3+9abc}{\prod\limits_{cyc}(a+b)}\geq6.$

Published on 09 Aug 2021 - 21:35

425

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Find the maximum of the value $F=x^3y+y^3z+z^3x$

Published on 26 Mar 2026 - 12:08

542

Views

Prove $x^2y + y^2z + z^2x \leq 4/27$, where $x+y+z=1, x\geq 0, y\geq 0, z\geq 0$

Published on 12 Aug 2021 - 19:56

154

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Symmetric sum of polynomials

Published on 14 Aug 2021 - 18:50

181

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If $f \in \Bbb Q[X_1, \dots ,X_n]$, is there a $Q \in \Bbb Q[X]$ such that $Q \circ f$ is a Symmetric Polynomial?

Published on 15 Aug 2021 - 2:48

94

Views

Bounds of an Expression

Published on 27 Mar 2026 - 23:01

508

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Algebraic independence of elementary symmetric polynomials

Published on 23 Feb 2026 - 4:38

144

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Degree of extension of symmetric function field

Published on 24 Aug 2021 - 5:22

List Question

Is there an expression for Hankel minors in terms of skew Schur polynomials?

Order on three real numbers given they are roots of a cubic, their sum and sum of pairwise product

Prove $a^2 + b^2 + c^2 + ab + bc +ca \ge 6$ given $a+b+c = 3$ for $a,b,c$ non-negative real.

Hard and non-trivial inequality with three variable reals

Discriminant of algebraic number field is $0$ or $1 \bmod 4$

Confusion on applying Newton formulae (not Newton's method) technique in finding roots

Interesting inequality with three positive reals which seems trivial

Prove that $\sum\limits_{cyc}\frac{a^2}{a^2+bc}+\frac{(a+b+c)^3+9abc}{\prod\limits_{cyc}(a+b)}\geq6.$

Find the maximum of the value $F=x^3y+y^3z+z^3x$

Prove $x^2y + y^2z + z^2x \leq 4/27$, where $x+y+z=1, x\geq 0, y\geq 0, z\geq 0$

Symmetric sum of polynomials

If $f \in \Bbb Q[X_1, \dots ,X_n]$, is there a $Q \in \Bbb Q[X]$ such that $Q \circ f$ is a Symmetric Polynomial?

Bounds of an Expression

Algebraic independence of elementary symmetric polynomials

Degree of extension of symmetric function field

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