List questions from symmetric-polynomials

Published on 24 Oct 2022 - 13:21

168

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$3$-var inequality: $\frac{bc}{\sqrt{a}+3}+\frac{ca}{\sqrt{b}+3}+\frac{ab}{\sqrt{c}+3} \leq \frac{3}{4}$ for $a+b+c=3$.

Published on 25 Mar 2026 - 23:42

215

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When does $\det\left(\begin{smallmatrix}1&1&1\\x_1&x_2&x_3\\x_2&x_3&x_1\end{smallmatrix}\right)=0$ imply $x_1=x_2=x_3$?

Published on 02 Nov 2022 - 8:05

105

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Polynomial ring of invariants and graphs

Published on 27 Mar 2026 - 23:13

25

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Derivation of the Macdonald operator $D_{n}(X;q,t)$

Published on 26 Mar 2026 - 9:17

35

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Is there a name for the polynomials of the form $\sum_{i = 0}^a x^{a - i}y^i - 1$?

Published on 30 Dec 2022 - 0:12

99

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Ring of invariants of symmetric group acting on ring of formal power series

Published on 25 Mar 2026 - 14:25

107

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Schur function of the conjugate representation

Published on 27 Mar 2026 - 23:01

64

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Characterization of finite fields

Published on 16 Jan 2023 - 20:09

380

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If $\alpha,\beta,\gamma,\delta$ are the roots of $x^4+px^3+qx^2+rx + s=0$, find in terms of $p,q,r,s$ the value of $\Sigma\frac{\alpha\beta}{\gamma }$

Published on 21 Jan 2023 - 12:25

53

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What is the largest value of $e_{k}(x_1,\cdots,x_n)$ not obtainable over $(\mathbb{N}^+)^n$?

Published on 27 Mar 2026 - 7:18

List Question

Number of terms of the polynomial $\prod_{1\leq i<j\leq n}( x_{i}+x_{j})$

$3$-var inequality: $\frac{bc}{\sqrt{a}+3}+\frac{ca}{\sqrt{b}+3}+\frac{ab}{\sqrt{c}+3} \leq \frac{3}{4}$ for $a+b+c=3$.

When does $\det\left(\begin{smallmatrix}1&1&1\\x_1&x_2&x_3\\x_2&x_3&x_1\end{smallmatrix}\right)=0$ imply $x_1=x_2=x_3$?

Polynomial ring of invariants and graphs

Derivation of the Macdonald operator $D_{n}(X;q,t)$

Is there a name for the polynomials of the form $\sum_{i = 0}^a x^{a - i}y^i - 1$?

Ring of invariants of symmetric group acting on ring of formal power series

Schur function of the conjugate representation

Characterization of finite fields

If $\alpha,\beta,\gamma,\delta$ are the roots of $x^4+px^3+qx^2+rx + s=0$, find in terms of $p,q,r,s$ the value of $\Sigma\frac{\alpha\beta}{\gamma }$

What is the largest value of $e_{k}(x_1,\cdots,x_n)$ not obtainable over $(\mathbb{N}^+)^n$?

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