List questions from symmetric-polynomials

Published on 25 Mar 2026 - 5:59

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An inequality involving real numbers

Published on 25 Mar 2026 - 17:45

255

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Finding real $(x,y)$ solutions that satisfies a system of equation.

Published on 14 Jul 2020 - 8:18

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In a triangle prove that $\mathrm{cosec}( A) +\mathrm{cosec}(B) +\mathrm{cosec}(C)\le \frac{2\sqrt 3}{9}\left (1+\frac Rr\right)^2$

Published on 26 Mar 2026 - 14:34

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An stronger inequality than in AoPS.

Published on 25 Mar 2026 - 17:38

169

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Express $x^2 y^2 + y^2 z^2 + z^2 x^2$ in the form of $x+y+z$, $xy+yz+zx$ and $xyz$?

Published on 15 Jul 2020 - 21:00

77

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On the value of a skew Schur function at the identity

Published on 25 Mar 2026 - 12:25

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Prove that in a triangle $\sum\limits_{cyc}\frac{w_bw_c}{w_a}\geq\frac{3}{4}\left(\sum\limits_{cyc}\frac{a^2w_a}{w_bw_c}\right)\geq\sqrt{3}s$

Published on 25 Mar 2026 - 17:41

120

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Prove that $(a b+b c+c a-1)^{2} \leq\left(a^{2}+1\right)\left(b^{2}+1\right)\left(c^{2}+1\right)$.

Published on 23 Jul 2020 - 13:58

79

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Contradiction on an Inequality

Published on 25 Mar 2026 - 20:34

95

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Inequality involving medians

Published on 25 Mar 2026 - 17:38

121

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Help with proving/disproving an inequality

Published on 29 Jul 2020 - 16:28

479

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Why weight of a monomial $X_1^{v_1}\cdots X_n^{v_n}$ is defined as $v_1+2v_2+\cdots + nv_n$, but not $v_1+\cdots+v_n$?

Published on 06 Jul 2016 - 4:26

350

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Fixed points of polynomial ring homomorphism

Published on 26 Mar 2026 - 4:51

160

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Name these symmetric polynomials over non-commutative variables...

Published on 08 Jul 2016 - 5:34

List Question

Reference for a real algebraic geometry problem

An inequality involving real numbers

Finding real $(x,y)$ solutions that satisfies a system of equation.

In a triangle prove that $\mathrm{cosec}( A) +\mathrm{cosec}(B) +\mathrm{cosec}(C)\le \frac{2\sqrt 3}{9}\left (1+\frac Rr\right)^2$

An stronger inequality than in AoPS.

Express $x^2 y^2 + y^2 z^2 + z^2 x^2$ in the form of $x+y+z$, $xy+yz+zx$ and $xyz$?

On the value of a skew Schur function at the identity

Prove that in a triangle $\sum\limits_{cyc}\frac{w_bw_c}{w_a}\geq\frac{3}{4}\left(\sum\limits_{cyc}\frac{a^2w_a}{w_bw_c}\right)\geq\sqrt{3}s$

Prove that $(a b+b c+c a-1)^{2} \leq\left(a^{2}+1\right)\left(b^{2}+1\right)\left(c^{2}+1\right)$.

Contradiction on an Inequality

Inequality involving medians

Help with proving/disproving an inequality

Why weight of a monomial $X_1^{v_1}\cdots X_n^{v_n}$ is defined as $v_1+2v_2+\cdots + nv_n$, but not $v_1+\cdots+v_n$?

Fixed points of polynomial ring homomorphism

Name these symmetric polynomials over non-commutative variables...

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