Question

Proving symmetric polynomial identity using generating functions

score 171 · Answer 1 · 2023-08-29 14:27:55

171

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Proving symmetric polynomial identity using generating functions

Published on 29 Aug 2023 - 14:27

score 41 · Answer 2 · 2023-09-01 00:51:55

41

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Concerning $\mathbb{C}(s_1,s_2,w)=\mathbb{C}(x,y)$, where $s_1,s_2$ are symmetric, $w$ is not symmetric

Published on 01 Sep 2023 - 0:51

score 41 · Answer 3 · 2023-09-02 12:36:19

41

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How to solve this symmetric equation system based on optic addition?

Published on 02 Sep 2023 - 12:36

score 138 · Answer 4 · 2026-03-25 06:06:22

138

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Coefficients of a symmetric product of polynomials with root of unity

Published on 25 Mar 2026 - 6:06

score 58 · Answer 5 · 2023-09-09 19:02:00

58

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Degrees of field extensions $[\mathbb{C}(x,y):\mathbb{C}(xy^n+x^ny)]$ and $[\mathbb{C}(x,y):\mathbb{C}(x+y^n,x^n+y)]$

Published on 09 Sep 2023 - 19:02

score 51 · Answer 6 · 2026-03-26 02:54:26

51

Views

inequality about elementary symmetric polynomials with real variables

Published on 26 Mar 2026 - 2:54

score 438 · Answer 7 · 2026-03-26 07:46:32

438

Views

How to prove $\sqrt{\frac{24a+13}{24a+13bc}}+\sqrt{\frac{24b+13}{24b+13ca}}+\sqrt{\frac{24c+13}{24c+13ab}}\ge 3$

Published on 26 Mar 2026 - 7:46

score 771 · Answer 8 · 2023-09-23 17:27:40

771

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Evaluating a value from symmetric polynomials

Published on 23 Sep 2023 - 17:27

score 581 · Answer 9 · 2023-09-24 20:07:39

581

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Is there a polynomial whose cube is a symmetric polynomial?

Published on 24 Sep 2023 - 20:07

score 197 · Answer 10 · 2023-09-29 15:54:41

197

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If $a_1,\ldots, a_n$ are numbers such that $a_1^k+\cdots + a_n^k = x$ for $1\leq k\leq n$, determine the product $a_1\cdots a_n$ in terms of $x$.

Published on 29 Sep 2023 - 15:54

score 128 · Answer 11 · 2023-10-01 23:46:02

128

Views

The system of elementary semi-symmetric polynomials followed from the polynomial equation

Published on 01 Oct 2023 - 23:46

score 82 · Answer 12 · 2023-10-07 11:54:50

82

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Uniform continuity of the roots of polynomials

Published on 07 Oct 2023 - 11:54

score 145 · Answer 13 · 2026-03-26 04:35:07

145

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$\frac34\le\sum_\text{cyc}\big(\frac{x}{x+1}\big)^2<2\ $ for $x,y,z>0$ and $xyz=1$.

Published on 26 Mar 2026 - 4:35

score 127 · Answer 14 · 2026-03-29 03:36:45

127

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$x^2 + y^2 + z^2 - 2xy - 2xz - 2yz$ is irreducible over $\mathbb{Z}[x, y, z]$

Published on 29 Mar 2026 - 3:36

score 135 · Answer 15 · 2023-10-17 17:12:40

135

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Let $a, b,c$ be positive real numbers such that $a+b+c=1,$ prove $(a + b) ^ 2 (1 + 2c)(2a + 3c)(2b + 3c) \ge54abc$

Published on 17 Oct 2023 - 17:12

List Question

Proving symmetric polynomial identity using generating functions

Concerning $\mathbb{C}(s_1,s_2,w)=\mathbb{C}(x,y)$, where $s_1,s_2$ are symmetric, $w$ is not symmetric

How to solve this symmetric equation system based on optic addition?

Coefficients of a symmetric product of polynomials with root of unity

Degrees of field extensions $[\mathbb{C}(x,y):\mathbb{C}(xy^n+x^ny)]$ and $[\mathbb{C}(x,y):\mathbb{C}(x+y^n,x^n+y)]$

inequality about elementary symmetric polynomials with real variables

How to prove $\sqrt{\frac{24a+13}{24a+13bc}}+\sqrt{\frac{24b+13}{24b+13ca}}+\sqrt{\frac{24c+13}{24c+13ab}}\ge 3$

Evaluating a value from symmetric polynomials

Is there a polynomial whose cube is a symmetric polynomial?

If $a_1,\ldots, a_n$ are numbers such that $a_1^k+\cdots + a_n^k = x$ for $1\leq k\leq n$, determine the product $a_1\cdots a_n$ in terms of $x$.

The system of elementary semi-symmetric polynomials followed from the polynomial equation

Uniform continuity of the roots of polynomials

$\frac34\le\sum_\text{cyc}\big(\frac{x}{x+1}\big)^2<2\ $ for $x,y,z>0$ and $xyz=1$.

$x^2 + y^2 + z^2 - 2xy - 2xz - 2yz$ is irreducible over $\mathbb{Z}[x, y, z]$

Let $a, b,c$ be positive real numbers such that $a+b+c=1,$ prove $(a + b) ^ 2 (1 + 2c)(2a + 3c)(2b + 3c) \ge54abc$

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