Question

A question about $G$- invariant polynomials.

score 88 · Answer 1 · 2021-10-08 13:51:41

88

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A question about $G$- invariant polynomials.

Published on 08 Oct 2021 - 13:51

score 331 · Answer 2 · 2026-03-25 19:03:08

331

Views

Algorithms for expressing symmetric polynomials as a polynomial in the elementary symmetric polynomials

Published on 25 Mar 2026 - 19:03

score 181 · Answer 3 · 2026-03-27 04:56:55

181

Views

Nice problem: Prove that: $ab+bc+ca \ge \sum{\sqrt{a^2+b^2+3}}$

Published on 27 Mar 2026 - 4:56

score 125 · Answer 4 · 2026-03-26 21:08:57

125

Views

Inequality without BW and Uvw, just AM GM

Published on 26 Mar 2026 - 21:08

score 157 · Answer 5 · 2026-03-25 18:49:37

157

Views

In triangle. Prove that: $2(a+b+c)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge9+\sum_{cyc}{\sqrt{17+\frac{4(b+c)((b-c)^2-a^2)}{abc}}}$

Published on 25 Mar 2026 - 18:49

score 241 · Answer 6 · 2026-03-26 21:10:20

241

Views

Prove that: $2(a+b+c)+\sqrt{ab}+\sqrt{bc}+\sqrt{ca}\ge\sqrt{5ab+4ac}+\sqrt{5bc+4ba}+\sqrt{5ca+4cb}$

Published on 26 Mar 2026 - 21:10

score 190 · Answer 7 · 2026-03-26 21:14:04

190

Views

Prove that $\frac{a^4+2a+b(2a^2+b)}{a^2(b^2+2a)}+\frac{b^4+2b+c(2b^2+c)}{b^2(c^2+2b)}+\frac{c^4+2c+a(2c^2+a)}{c^2(a^2+2c)}\ge 6$

Published on 26 Mar 2026 - 21:14

score 213 · Answer 8 · 2021-10-21 21:11:44

213

Views

Local max of ratio of elementary symmetric polynomials

Published on 21 Oct 2021 - 21:11

score 52 · Answer 9 · 2026-03-27 00:03:47

52

Views

Definition of Macdonald polynomial $P_\lambda^{\mathfrak{g}}$ associated to a Lie algebra $\mathfrak{g}$ (unlike $P_\lambda$)

Published on 27 Mar 2026 - 0:03

score 160 · Answer 10 · 2026-03-27 01:46:05

160

Views

Schur polynomial of partition (1,0)

Published on 27 Mar 2026 - 1:46

score 52 · Answer 11 · 2026-03-27 02:02:57

52

Views

General formulation of polynomial invariants.

Published on 27 Mar 2026 - 2:02

score 113 · Answer 12 · 2021-11-24 22:13:32

113

Views

How does the fundamental theorem of symmetric polynomials imply that this number is rational?

Published on 24 Nov 2021 - 22:13

score 24 · Answer 13 · 2021-11-28 18:32:13

24

Views

Is it possible to obtain roots from the weighted sum of other polynomials in their root form?

Published on 28 Nov 2021 - 18:32

score 131 · Answer 14 · 2021-11-29 19:52:34

131

Views

Reciprocal binomial coefficient polynomial evaluation

Published on 29 Nov 2021 - 19:52

score 43 · Answer 15 · 2021-11-29 22:15:17

43

Views

Root transformation to make normalized coefficient match

Published on 29 Nov 2021 - 22:15

List Question

A question about $G$- invariant polynomials.

Algorithms for expressing symmetric polynomials as a polynomial in the elementary symmetric polynomials

Nice problem: Prove that: $ab+bc+ca \ge \sum{\sqrt{a^2+b^2+3}}$

Inequality without BW and Uvw, just AM GM

In triangle. Prove that: $2(a+b+c)\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\ge9+\sum_{cyc}{\sqrt{17+\frac{4(b+c)((b-c)^2-a^2)}{abc}}}$

Prove that: $2(a+b+c)+\sqrt{ab}+\sqrt{bc}+\sqrt{ca}\ge\sqrt{5ab+4ac}+\sqrt{5bc+4ba}+\sqrt{5ca+4cb}$

Prove that $\frac{a^4+2a+b(2a^2+b)}{a^2(b^2+2a)}+\frac{b^4+2b+c(2b^2+c)}{b^2(c^2+2b)}+\frac{c^4+2c+a(2c^2+a)}{c^2(a^2+2c)}\ge 6$

Local max of ratio of elementary symmetric polynomials

Definition of Macdonald polynomial $P_\lambda^{\mathfrak{g}}$ associated to a Lie algebra $\mathfrak{g}$ (unlike $P_\lambda$)

Schur polynomial of partition (1,0)

General formulation of polynomial invariants.

How does the fundamental theorem of symmetric polynomials imply that this number is rational?

Is it possible to obtain roots from the weighted sum of other polynomials in their root form?

Reciprocal binomial coefficient polynomial evaluation

Root transformation to make normalized coefficient match

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