Question

Symmetric polynomials in some variables

score 125 · Answer 1 · 2014-06-23 15:27:48

125

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Symmetric polynomials in some variables

Published on 23 Jun 2014 - 15:27

score 123 · Answer 2 · 2014-06-24 22:16:15

123

Views

Combinatorics and symmetric functions

Published on 24 Jun 2014 - 22:16

score 452 · Answer 3 · 2014-07-11 06:40:14

452

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Prove $\sum\limits_{\mathrm{cyc}}\sqrt{a^2+bc}\leq{3\over2}(a+b+c)$ with $a,b,c$ are nonnegative

Published on 11 Jul 2014 - 6:40

score 1.3k · Answer 4 · 2014-07-12 06:39:12

1.3k

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natural isomorphism of polynomial functions on $V$ and $S(V^*)$

Published on 12 Jul 2014 - 6:39

score 203 · Answer 5 · 2026-03-25 07:46:10

203

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Seeking concise proof: $\frac18(a^2+b^2)(b^2+c^2)(c^2+a^2)\ge\frac1{27}(ab+bc+ca)^3$, where $a$, $b$, $c$ are positive numbers

Published on 25 Mar 2026 - 7:46

score 151 · Answer 6 · 2014-07-18 15:52:55

151

Views

Basic Manipulation of Adams operations in R(G)

Published on 18 Jul 2014 - 15:52

score 2k · Answer 7 · 2014-07-18 16:30:59

2k

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How to solve a system of three nonlinear equation in a simple way

Published on 18 Jul 2014 - 16:30

score 189 · Answer 8 · 2026-03-25 11:07:03

189

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Dimension of the Image of Young Projectors corresponding to Tensor factors.

Published on 25 Mar 2026 - 11:07

score 191 · Answer 9 · 2014-07-23 15:55:32

191

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If $a+b+c+d=4$, then $\sum\frac{1}{a+3}\le \frac{1}{abcd}$

Published on 23 Jul 2014 - 15:55

score 600 · Answer 10 · 2026-03-25 03:04:10

600

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Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$

Published on 25 Mar 2026 - 3:04

score 465 · Answer 11 · 2026-03-25 12:50:50

465

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If the sum of cubes of $a,b,c,d$ is $1$, then $\frac{1}{1-bcd}+\frac{1}{1-cda}+\frac{1}{1-dab}+\frac{1}{1-abc}\le \frac{16}{3}$

Published on 25 Mar 2026 - 12:50

score 3.4k · Answer 12 · 2014-08-12 07:20:01

3.4k

Views

Sum of cubes of roots of a quartic equation

Published on 12 Aug 2014 - 7:20

score 343 · Answer 13 · 2014-08-25 21:05:11

343

Views

Writing sum of square roots with symmetric polynomials

Published on 25 Aug 2014 - 21:05

score 55 · Answer 14 · 2014-09-09 11:07:27

55

Views

Perform $x_1^3+x_2^3+\cdots+x_n^3$ by basic symetric polynomials.

Published on 09 Sep 2014 - 11:07

score 49 · Answer 15 · 2014-09-09 15:46:28

49

Views

Necessary condition for symmetric sums

Published on 09 Sep 2014 - 15:46

List Question

Symmetric polynomials in some variables

Combinatorics and symmetric functions

Prove $\sum\limits_{\mathrm{cyc}}\sqrt{a^2+bc}\leq{3\over2}(a+b+c)$ with $a,b,c$ are nonnegative

natural isomorphism of polynomial functions on $V$ and $S(V^*)$

Seeking concise proof: $\frac18(a^2+b^2)(b^2+c^2)(c^2+a^2)\ge\frac1{27}(ab+bc+ca)^3$, where $a$, $b$, $c$ are positive numbers

Basic Manipulation of Adams operations in R(G)

How to solve a system of three nonlinear equation in a simple way

Dimension of the Image of Young Projectors corresponding to Tensor factors.

If $a+b+c+d=4$, then $\sum\frac{1}{a+3}\le \frac{1}{abcd}$

Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$

If the sum of cubes of $a,b,c,d$ is $1$, then $\frac{1}{1-bcd}+\frac{1}{1-cda}+\frac{1}{1-dab}+\frac{1}{1-abc}\le \frac{16}{3}$

Sum of cubes of roots of a quartic equation

Writing sum of square roots with symmetric polynomials

Perform $x_1^3+x_2^3+\cdots+x_n^3$ by basic symetric polynomials.

Necessary condition for symmetric sums

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