Question

A way to read off $\deg \phi(P)$ directly from $P$ where $\phi:\mathbb{C}[x_1, \cdots, x_n]^{\mathfrak{S}_n}\to \mathbb{C}[e_1, \cdots, e_n]$?

score 26 · Answer 1 · 2016-10-17 21:08:32

A way to read off $\deg \phi(P)$ directly from $P$ where $\phi:\mathbb{C}[x_1, \cdots, x_n]^{\mathfrak{S}_n}\to \mathbb{C}[e_1, \cdots, e_n]$?

score 88 · Answer 2 · 2026-03-25 11:11:47

88

Views

Non - symetric inequality in 3 variables

Published on 25 Mar 2026 - 11:11

score 67 · Answer 3 · 2016-10-23 12:56:29

67

Views

If $y, z \in B$ are integral over $A$ then so are $z+y$ and $zy$.

Published on 23 Oct 2016 - 12:56

score 1.1k · Answer 4 · 2026-03-25 19:07:13

1.1k

Views

Prove inequality $ \frac{(x+y-1)^2}{z}+\frac{(x+z-1)^2}{y}+\frac{(y+z-1)^2}{x} \geq 12 $

Published on 25 Mar 2026 - 19:07

score 203 · Answer 5 · 2016-10-29 15:50:09

203

Views

Maximum value of symmetric elementary polynomials?

Published on 29 Oct 2016 - 15:50

score 123 · Answer 6 · 2026-03-27 10:12:03

123

Views

Find the value of $\sum\limits_{\mathrm{cyc}}\frac{1}{xy+z-1}$ if $(x,y,z)$ are the roots of some given cubic polynomial

Published on 27 Mar 2026 - 10:12

score 160 · Answer 7 · 2016-11-17 03:01:09

160

Views

Find three distinct triples (a, b, c) consisting of rational numbers that satisfy $a^2+b^2+c^2 =1$ and $a+b+c= \pm 1$.

Published on 17 Nov 2016 - 3:01

score 294 · Answer 8 · 2016-11-19 17:17:02

294

Views

Proof that in a sequence of vectors of length N, the Nth vector must be zero

Published on 19 Nov 2016 - 17:17

score 1.2k · Answer 9 · 2016-11-21 01:13:30

1.2k

Views

Let $a,b,c$ be the roots of $x^3 - x - 1= 0$ find $a^5 + b^5 + c^5$

Published on 21 Nov 2016 - 1:13

score 42 · Answer 10 · 2026-03-27 16:37:19

42

Views

System of 2 non-linear equations

Published on 27 Mar 2026 - 16:37

score 124 · Answer 11 · 2016-11-23 16:45:06

124

Views

System of four equations of four variables including second powers.

Published on 23 Nov 2016 - 16:45

score 153 · Answer 12 · 2016-11-28 10:21:37

153

Views

If $x + y + z = 0$ then $x\left(\frac1y+\frac1z\right)+y\left(\frac1z+\frac1x\right)+z\left(\frac1x+\frac1y\right) = -3$

Published on 28 Nov 2016 - 10:21

score 896 · Answer 13 · 2016-11-28 10:25:07

896

Views

A non-Vandermonde matrix with Vandermonde-like determinant?

Published on 28 Nov 2016 - 10:25

score 88 · Answer 14 · 2016-11-30 10:04:11

88

Views

question of macdonald'book "symmetric functions and hall polynomials' on page 3

Published on 30 Nov 2016 - 10:04

score 274 · Answer 15 · 2026-03-26 06:27:50

274

Views

Alternating polynomials under $S_4$-action: Version of Chevalley's Theorem

Published on 26 Mar 2026 - 6:27

List Question

A way to read off $\deg \phi(P)$ directly from $P$ where $\phi:\mathbb{C}[x_1, \cdots, x_n]^{\mathfrak{S}_n}\to \mathbb{C}[e_1, \cdots, e_n]$?

Non - symetric inequality in 3 variables

If $y, z \in B$ are integral over $A$ then so are $z+y$ and $zy$.

Prove inequality $ \frac{(x+y-1)^2}{z}+\frac{(x+z-1)^2}{y}+\frac{(y+z-1)^2}{x} \geq 12 $

Maximum value of symmetric elementary polynomials?

Find the value of $\sum\limits_{\mathrm{cyc}}\frac{1}{xy+z-1}$ if $(x,y,z)$ are the roots of some given cubic polynomial

Find three distinct triples (a, b, c) consisting of rational numbers that satisfy $a^2+b^2+c^2 =1$ and $a+b+c= \pm 1$.

Proof that in a sequence of vectors of length N, the Nth vector must be zero

Let $a,b,c$ be the roots of $x^3 - x - 1= 0$ find $a^5 + b^5 + c^5$

System of 2 non-linear equations

System of four equations of four variables including second powers.

If $x + y + z = 0$ then $x\left(\frac1y+\frac1z\right)+y\left(\frac1z+\frac1x\right)+z\left(\frac1x+\frac1y\right) = -3$

A non-Vandermonde matrix with Vandermonde-like determinant?

question of macdonald'book "symmetric functions and hall polynomials' on page 3

Alternating polynomials under $S_4$-action: Version of Chevalley's Theorem

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