Question

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

score 366 · Answer 1 · 2026-03-20 01:51:33

366

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

Published on 20 Mar 2026 - 1:51

score 1.1k · Answer 2 · 2018-04-06 17:49:34

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 06 Apr 2018 - 17:49

score 44 · Answer 3 · 2026-03-25 04:35:20

44

Views

Symmetric polynomials - real versus complex...

Published on 25 Mar 2026 - 4:35

score 985 · Answer 4 · 2018-04-09 08:24:30

985

Views

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

Published on 09 Apr 2018 - 8:24

score 670 · Answer 5 · 2026-03-22 05:56:56

670

Views

prove this inequality by $abc=1$

Published on 22 Mar 2026 - 5:56

score 169 · Answer 6 · 2018-04-12 01:57:10

169

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 12 Apr 2018 - 1:57

score 103 · Answer 7 · 2026-03-25 03:21:28

103

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 25 Mar 2026 - 3:21

score 92 · Answer 8 · 2018-04-20 21:13:37

92

Views

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

Published on 20 Apr 2018 - 21:13

score 507 · Answer 9 · 2018-04-21 17:21:41

507

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 21 Apr 2018 - 17:21

score 63 · Answer 10 · 2018-04-22 02:55:08

63

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 22 Apr 2018 - 2:55

score 48 · Answer 11 · 2018-04-22 11:06:07

48

Views

Integral Representation of Symmetric Polynomial Sums

Published on 22 Apr 2018 - 11:06

score 91 · Answer 12 · 2018-04-27 01:08:56

91

Views

A simple Inequality?

Published on 27 Apr 2018 - 1:08

score 401 · Answer 13 · 2018-04-29 13:21:43

401

Views

Deriving Dummit's sextic resolvent for quintic polynomials

Published on 29 Apr 2018 - 13:21

score 102 · Answer 14 · 2018-04-30 14:19:48

102

Views

Proof of a Symmetric-Like Expression

Published on 30 Apr 2018 - 14:19

score 182 · Answer 15 · 2026-03-17 09:25:46

182

Views

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

Published on 17 Mar 2026 - 9:25

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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