Question

Inequality involving cyclic sums (Muirhead? Schur? Something else?)

score 375 · Answer 1 · 2026-04-29 12:44:26

375

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Inequality involving cyclic sums (Muirhead? Schur? Something else?)

Published on 29 Apr 2026 - 12:44

score 1.1k · Answer 2 · 2026-04-13 23:47:31

1.1k

Views

Show that the cycle decomposition of a permutation can be recovered by considering the orbits of the action of its cyclic group on $\{1, 2, ..., n\}$

Published on 13 Apr 2026 - 23:47

score 46 · Answer 3 · 2026-03-28 04:24:44

46

Views

Symmetric polynomials - real versus complex...

Published on 28 Mar 2026 - 4:24

score 990 · Answer 4 · 2026-04-17 10:17:32

990

Views

Determine the value of $ax^5 + by^5$ given that $a$, $b$, $x$, and $y$ satisfy the following system:

Published on 17 Apr 2026 - 10:17

score 680 · Answer 5 · 2026-05-07 07:17:02

680

Views

prove this inequality by $abc=1$

Published on 07 May 2026 - 7:17

score 172 · Answer 6 · 2026-04-15 11:25:11

172

Views

Solve system:$yz(y+z-x)= a(x+y+z)\\ zx(z+x-y)= b(x+y+z)\\ xy(x+y-z)= c(x+y+z)$

Published on 15 Apr 2026 - 11:25

score 105 · Answer 7 · 2026-04-17 07:57:24

105

Views

Small confusion when solving the system of nonlinear equations $\begin{cases} 3y-2xy-y^2=0\\ 3x-x^2-2xy =0 \end{cases}$

Published on 17 Apr 2026 - 7:57

score 95 · Answer 8 · 2026-04-14 02:52:55

95

Views

How are these two monomials $u_1u_2^2$ and $u_2u_3^2$ in the same orbit?

Published on 14 Apr 2026 - 2:52

score 510 · Answer 9 · 2026-04-16 20:08:37

510

Views

Suppose $ x+y+z=0 $. Show that $ \frac{x^5+y^5+z^5}{5}=\frac{x^2+y^2+z^2}{2}\times\frac{x^3+y^3+z^3}{3} $.

Published on 16 Apr 2026 - 20:08

score 66 · Answer 10 · 2026-04-16 06:27:24

66

Views

let $a,b,c$ be real numbers (not necessarily positive) for which $\min(a+b,b+c,c+a)\ge 2$. Show that $(a+b+c)^3 \ge a^3 + b^3 + c^3 + 24$

Published on 16 Apr 2026 - 6:27

score 51 · Answer 11 · 2026-04-14 15:20:37

51

Views

Integral Representation of Symmetric Polynomial Sums

Published on 14 Apr 2026 - 15:20

score 96 · Answer 12 · 2026-04-14 02:13:08

96

Views

A simple Inequality?

Published on 14 Apr 2026 - 2:13

score 404 · Answer 13 · 2026-04-14 12:40:48

404

Views

Deriving Dummit's sextic resolvent for quintic polynomials

Published on 14 Apr 2026 - 12:40

score 106 · Answer 14 · 2026-04-10 07:27:21

106

Views

Proof of a Symmetric-Like Expression

Published on 10 Apr 2026 - 7:27

score 190 · Answer 15 · 2026-05-05 04:17:03

190

Views

If $x+y+z=2$ prove that $\sum_{cyc}\frac{1}{\sqrt{x^2+y^2}}\ge2+\frac{1}{\sqrt{2}}$

Published on 05 May 2026 - 4:17

List Question

Inequality involving cyclic sums (Muirhead? Schur? Something else?)

Show that the cycle decomposition of a permutation can be recovered by considering the orbits of the action of its cyclic group on $\{1, 2, ..., n\}$

Symmetric polynomials - real versus complex...

Determine the value of $ax^5 + by^5$ given that $a$, $b$, $x$, and $y$ satisfy the following system:

prove this inequality by $abc=1$

Solve system:$yz(y+z-x)= a(x+y+z)\\ zx(z+x-y)= b(x+y+z)\\ xy(x+y-z)= c(x+y+z)$

Small confusion when solving the system of nonlinear equations $\begin{cases} 3y-2xy-y^2=0\\ 3x-x^2-2xy =0 \end{cases}$

How are these two monomials $u_1u_2^2$ and $u_2u_3^2$ in the same orbit?

Suppose $ x+y+z=0 $. Show that $ \frac{x^5+y^5+z^5}{5}=\frac{x^2+y^2+z^2}{2}\times\frac{x^3+y^3+z^3}{3} $.

let $a,b,c$ be real numbers (not necessarily positive) for which $\min(a+b,b+c,c+a)\ge 2$. Show that $(a+b+c)^3 \ge a^3 + b^3 + c^3 + 24$

Integral Representation of Symmetric Polynomial Sums

A simple Inequality?

Deriving Dummit's sextic resolvent for quintic polynomials

Proof of a Symmetric-Like Expression

If $x+y+z=2$ prove that $\sum_{cyc}\frac{1}{\sqrt{x^2+y^2}}\ge2+\frac{1}{\sqrt{2}}$

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