List questions from symmetric-polynomials

Published on 14 Sep 2017 - 18:45

61

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Extension of Newton-Girard to matrix-indexed monomials

Published on 16 Sep 2017 - 21:49

150

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Given $a^3+b^3+c^3=(a+b+c)^3$, show that $a^{2n+1}+b^{2n+1}+c^{2n+1}=(a+b+c)^{2n+1}$

Published on 17 Sep 2017 - 17:32

47

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When is the solution to a system of equations a convex combination.

Published on 20 Sep 2017 - 21:56

183

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Rules to compute with elementary symmetric polynomials

Published on 21 Sep 2017 - 17:41

242

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Compute $\sum r_1^4$ as a linear combination of elementary symmetric polynomials

Published on 22 Sep 2017 - 7:46

452

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$(xy+yz+zx)(1+6xyz) \geq 11xyz$

Published on 25 Mar 2026 - 19:06

54

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A corollary from the fact that every symmetric polynomial could be written as a polynomial in the elementary ones

Published on 27 Sep 2017 - 19:38

30

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Show that $G \cong D_4$.

Published on 02 Oct 2017 - 7:11

165

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Expressing $\sum _{i=1}^n x_i^3\,+\,\sum _{i=1}^n\sum _{j=1}^n x_i^2 x_j$ as a polynomial in elementary symmetric polynomials

Published on 02 Oct 2017 - 8:11

260

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Minimum value of $S=\frac{3a}{b+c}+\frac{4b}{a+c}+\frac{5c}{a+b}$

Published on 26 Mar 2026 - 17:13

37

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Prove that all zeroes are equal

Published on 05 Oct 2017 - 7:27

729

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Prove that the discriminant of a degree $n$ polynomial f is a polynomial of degree $2n - 2$ in the coefficients of $f$

Published on 26 Mar 2026 - 0:53

77

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Schur symmetric functions

Published on 26 Mar 2026 - 17:18

115

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Prove that $ \frac{x}{yz} + \frac{y}{xz} + \frac{z}{xy} \geq \frac{1}{x} + \frac{1}{y} + \frac{1}{z} $

Published on 25 Mar 2026 - 21:51

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smart manipulation of roots

Extension of Newton-Girard to matrix-indexed monomials

Given $a^3+b^3+c^3=(a+b+c)^3$, show that $a^{2n+1}+b^{2n+1}+c^{2n+1}=(a+b+c)^{2n+1}$

When is the solution to a system of equations a convex combination.

Rules to compute with elementary symmetric polynomials

Compute $\sum r_1^4$ as a linear combination of elementary symmetric polynomials

$(xy+yz+zx)(1+6xyz) \geq 11xyz$

A corollary from the fact that every symmetric polynomial could be written as a polynomial in the elementary ones

Show that $G \cong D_4$.

Expressing $\sum _{i=1}^n x_i^3\,+\,\sum _{i=1}^n\sum _{j=1}^n x_i^2 x_j$ as a polynomial in elementary symmetric polynomials

Minimum value of $S=\frac{3a}{b+c}+\frac{4b}{a+c}+\frac{5c}{a+b}$

Prove that all zeroes are equal

Prove that the discriminant of a degree $n$ polynomial f is a polynomial of degree $2n - 2$ in the coefficients of $f$

Schur symmetric functions

Prove that $ \frac{x}{yz} + \frac{y}{xz} + \frac{z}{xy} \geq \frac{1}{x} + \frac{1}{y} + \frac{1}{z} $

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