List questions from symmetric-polynomials

Published on 14 Jan 2020 - 16:52

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How to prove $a^3+b^3+c^3+d^3+3\left(a+b+c+d\right) \geq 14+2abcd$ when $a^2+b^2+c^2+d^2=4$

Published on 15 Jan 2020 - 23:30

40

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Not really sure how to proceed further with this inequality

Published on 16 Jan 2020 - 5:00

828

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$a^3 + b^3 + c^3 = 3abc$ , can this be true only when $a+b+c = 0$ or $a=b=c$, or can it be true in any other case?

Published on 19 Jan 2020 - 11:58

39

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Algebraic identity for summing all arrangements of n choose k terms

Published on 25 Mar 2026 - 11:06

305

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A second formula for the dimension of the symmetric tensor product? ... (No)

Published on 26 Mar 2026 - 22:15

149

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Proof of Theorem 11.2 in Alan Baker's A Comprehensive Course in Number Theory

Published on 22 Jan 2020 - 13:37

204

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Cyclic Inequality $(x^8+1)(x^4+1)(y^8+1)(y^4+1)(z^8+1)(z^4+1)≥((x^2+1)(y^2+1)(z^2+1))^2$

Published on 25 Mar 2026 - 14:35

94

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For real $a$, $b$, $c$ in $(0,1)$, if $a+b+c=2$, then $\frac{a}{1-a}\times\frac{b}{1-b}\times\frac{c}{1-c}\geq 8$

Published on 27 Jan 2020 - 16:12

103

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How to prove this symmetric polynomial identity

Published on 28 Jan 2020 - 19:55

255

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A nontrvial inequality $\sum\limits_{\rm cyc}a^2 c(4a-3b-c)^2\ge 20abc\sum\limits_{\rm cyc}a(a-b)$

Published on 25 Mar 2026 - 4:43

174

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Homogeneous products of variables

Published on 30 Jan 2020 - 7:59

150

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Another asymmetric inequality $5+\frac{3(a^2+2b^2+c^2)}{(a+b)(b+c)} \geq \frac{9(a+b)(b+c)(c+a)}{(a+b+c)(ab+bc+ca)}$

Published on 25 Mar 2026 - 9:43

67

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the $\max$ of $\min$

Published on 26 Mar 2026 - 21:39

179

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Properties of the map $(x,y,z)\to (x+y+z,xy+yz+zx,xyz)$

Published on 08 Feb 2020 - 8:09

List Question

Expressions of higher Casimir operators

How to prove $a^3+b^3+c^3+d^3+3\left(a+b+c+d\right) \geq 14+2abcd$ when $a^2+b^2+c^2+d^2=4$

Not really sure how to proceed further with this inequality

$a^3 + b^3 + c^3 = 3abc$ , can this be true only when $a+b+c = 0$ or $a=b=c$, or can it be true in any other case?

Algebraic identity for summing all arrangements of n choose k terms

A second formula for the dimension of the symmetric tensor product? ... (No)

Proof of Theorem 11.2 in Alan Baker's A Comprehensive Course in Number Theory

Cyclic Inequality $(x^8+1)(x^4+1)(y^8+1)(y^4+1)(z^8+1)(z^4+1)≥((x^2+1)(y^2+1)(z^2+1))^2$

For real $a$, $b$, $c$ in $(0,1)$, if $a+b+c=2$, then $\frac{a}{1-a}\times\frac{b}{1-b}\times\frac{c}{1-c}\geq 8$

How to prove this symmetric polynomial identity

A nontrvial inequality $\sum\limits_{\rm cyc}a^2 c(4a-3b-c)^2\ge 20abc\sum\limits_{\rm cyc}a(a-b)$

Homogeneous products of variables

Another asymmetric inequality $5+\frac{3(a^2+2b^2+c^2)}{(a+b)(b+c)} \geq \frac{9(a+b)(b+c)(c+a)}{(a+b+c)(ab+bc+ca)}$

the $\max$ of $\min$

Properties of the map $(x,y,z)\to (x+y+z,xy+yz+zx,xyz)$

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