Question

Homogeneous fourth degree inequality : $\sum x_i^2x_j^2 +6x_1x_2x_3x_4 \geq\sum x_ix_jx_k^2$

score 114 · Answer 1 · 2026-03-23 10:25:32

114

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Homogeneous fourth degree inequality : $\sum x_i^2x_j^2 +6x_1x_2x_3x_4 \geq\sum x_ix_jx_k^2$

Published on 23 Mar 2026 - 10:25

score 292 · Answer 2 · 2018-02-19 18:05:26

292

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An identity of complete homogeneous symmetric polynomials $\sum_{k=1}^\infty k h_k(X)h_k(Y) t^{k-1}$

Published on 19 Feb 2018 - 18:05

score 529 · Answer 3 · 2026-03-17 07:14:19

529

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Schur polynomials on 1's and -1's

Published on 17 Mar 2026 - 7:14

score 2.4k · Answer 4 · 2018-02-23 15:46:50

2.4k

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Prove that every symmetric polynomial can be written in terms of the elementary symmetric polynomials

Published on 23 Feb 2018 - 15:46

score 160 · Answer 5 · 2018-02-23 21:52:07

160

Views

$\sum a=8$, $\sum ab=12$ where $a,b,c,d\in\mathbb{R}$. Find the maximum value of $d$.

Published on 23 Feb 2018 - 21:52

score 64 · Answer 6 · 2018-02-24 04:46:20

64

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Cauchy can't be applied on this inequality for this condition of a, b, c

Published on 24 Feb 2018 - 4:46

score 179 · Answer 7 · 2018-02-27 05:56:04

179

Views

Show that $\frac{1}{a^n+b^n+c^n} = \frac{1}{a^n} + \frac{1}{b^n} + \frac{1}{c^n}$

Published on 27 Feb 2018 - 5:56

score 151 · Answer 8 · 2018-02-28 13:14:20

151

Views

Prove $\Delta=\left|\begin{smallmatrix} 3x&-x+y&-x+z\\ -y+x&3y&-y+z\\-z+x&-z+y&3z\end{smallmatrix}\right|=3(x+y+z)(xy+yz+zx)$

Published on 28 Feb 2018 - 13:14

score 92 · Answer 9 · 2026-03-22 13:46:18

92

Views

Positivity of symmetric sums of $x$, $y$, $z$

Published on 22 Mar 2026 - 13:46

score 107 · Answer 10 · 2018-03-03 07:02:46

107

Views

Easier way to identify a 3 variable determinant as symmetric polynomial

Published on 03 Mar 2018 - 7:02

score 160 · Answer 11 · 2018-03-04 08:41:39

160

Views

Factorize $\det\left[\begin{smallmatrix}yz-x^2&zx-y^2&xy-z^2\\zx-y^2&xy-z^2&yz-x^2\\xy-z^2&yz-x^2&zx-y^2\end{smallmatrix}\right]$ using factor theorem

Published on 04 Mar 2018 - 8:41

score 371 · Answer 12 · 2026-03-19 16:06:55

371

Views

Proving an identity for complete homogenous symmetric polynomials

Published on 19 Mar 2026 - 16:06

score 53 · Answer 13 · 2026-03-22 07:54:33

53

Views

Solving a System of Equations for ( a , b , c )

Published on 22 Mar 2026 - 7:54

score 40 · Answer 14 · 2018-03-29 17:36:36

40

Views

Given a power sum symmetric polynomial $p_n = an^n/n!$, to show that the generating function $P(t) = ae^x/(1-x)$, for $t = xe^{-x}$

Published on 29 Mar 2018 - 17:36

score 291 · Answer 15 · 2018-03-31 17:03:01

291

Views

Finding the elementary and power sum symmetric polynomial given complete symmetric polynomial

Published on 31 Mar 2018 - 17:03

List Question

Homogeneous fourth degree inequality : $\sum x_i^2x_j^2 +6x_1x_2x_3x_4 \geq\sum x_ix_jx_k^2$

An identity of complete homogeneous symmetric polynomials $\sum_{k=1}^\infty k h_k(X)h_k(Y) t^{k-1}$

Schur polynomials on 1's and -1's

Prove that every symmetric polynomial can be written in terms of the elementary symmetric polynomials

$\sum a=8$, $\sum ab=12$ where $a,b,c,d\in\mathbb{R}$. Find the maximum value of $d$.

Cauchy can't be applied on this inequality for this condition of a, b, c

Show that $\frac{1}{a^n+b^n+c^n} = \frac{1}{a^n} + \frac{1}{b^n} + \frac{1}{c^n}$

Prove $\Delta=\left|\begin{smallmatrix} 3x&-x+y&-x+z\\ -y+x&3y&-y+z\\-z+x&-z+y&3z\end{smallmatrix}\right|=3(x+y+z)(xy+yz+zx)$

Positivity of symmetric sums of $x$, $y$, $z$

Easier way to identify a 3 variable determinant as symmetric polynomial

Factorize $\det\left[\begin{smallmatrix}yz-x^2&zx-y^2&xy-z^2\\zx-y^2&xy-z^2&yz-x^2\\xy-z^2&yz-x^2&zx-y^2\end{smallmatrix}\right]$ using factor theorem

Proving an identity for complete homogenous symmetric polynomials

Solving a System of Equations for ( a , b , c )

Given a power sum symmetric polynomial $p_n = an^n/n!$, to show that the generating function $P(t) = ae^x/(1-x)$, for $t = xe^{-x}$

Finding the elementary and power sum symmetric polynomial given complete symmetric polynomial

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