List questions from symmetric-polynomials

Published on 31 Jul 2017 - 13:49

65

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Symmetric elements in $k(x_1,y_1,\ldots,x_n,y_n)$ w.r.t. $\alpha_n: x_i \leftrightarrow y_i$

Published on 02 Aug 2017 - 8:53

135

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Hook-content polynomial

Published on 25 Mar 2026 - 20:09

1.3k

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Please help explain how "Any symmetric sum can be written as a Polynomial of the elementary symmetric sum functions"

Published on 08 Aug 2017 - 16:28

359

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If $a+b+c=3$ show $a^2+b^2+c^2 \leq (27-15\sqrt{3})\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$

Published on 26 Mar 2026 - 12:50

98

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Has this variant on multiplication by a natural number been studied before?

Published on 17 Aug 2017 - 15:48

56

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If $f(x_1,\ldots,x_n)/g(x_1,\ldots,x_n) \in F(x_1,\ldots,x_n)$ is symmetric, then both $f$ and $g$ are symmetric

Published on 20 Aug 2017 - 9:40

132

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Fixed field of $A_n$ is $F(p_1,\ldots,p_n,\Delta)$

Published on 20 Aug 2017 - 16:16

60

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Computing symmetric form of certain polynomials

Published on 23 Aug 2017 - 13:02

51

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Solving system of equations be eliminating

Published on 24 Aug 2017 - 19:46

142

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Prove that inequality $\sum _{cyc}\frac{a^2+b^2}{a+b}\le \frac{3\left(a^2+b^2+c^2\right)}{a+b+c}$

Published on 01 Sep 2017 - 11:22

98

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Do these summations satisfy modular properties

Published on 26 Mar 2026 - 9:36

94

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Murnaghan-Nakayama rule for general dimension of a hook

Published on 25 Mar 2026 - 20:13

133

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$a^2 + b^2 + c^2 = 3$, prove that $a + b + c \ge ab + bc + ac$

Published on 14 Sep 2017 - 15:39

472

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$\frac{3}{abc} \ge a + b + c$, prove that $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \ge a + b + c$

Published on 14 Sep 2017 - 16:54

List Question

Elementary symmetric functions of a number field embedding

Symmetric elements in $k(x_1,y_1,\ldots,x_n,y_n)$ w.r.t. $\alpha_n: x_i \leftrightarrow y_i$

Hook-content polynomial

Please help explain how "Any symmetric sum can be written as a Polynomial of the elementary symmetric sum functions"

If $a+b+c=3$ show $a^2+b^2+c^2 \leq (27-15\sqrt{3})\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)$

Has this variant on multiplication by a natural number been studied before?

If $f(x_1,\ldots,x_n)/g(x_1,\ldots,x_n) \in F(x_1,\ldots,x_n)$ is symmetric, then both $f$ and $g$ are symmetric

Fixed field of $A_n$ is $F(p_1,\ldots,p_n,\Delta)$

Computing symmetric form of certain polynomials

Solving system of equations be eliminating

Prove that inequality $\sum _{cyc}\frac{a^2+b^2}{a+b}\le \frac{3\left(a^2+b^2+c^2\right)}{a+b+c}$

Do these summations satisfy modular properties

Murnaghan-Nakayama rule for general dimension of a hook

$a^2 + b^2 + c^2 = 3$, prove that $a + b + c \ge ab + bc + ac$

$\frac{3}{abc} \ge a + b + c$, prove that $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} \ge a + b + c$

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