Question

Hall-Littlewood polynomials and elementary symmetric functions-- Chapter III (2.8) in Macdonald's "Symmetric Functions and Hall Polynomials"

score 205 · Answer 1 · 2026-03-26 22:16:18

205

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Hall-Littlewood polynomials and elementary symmetric functions-- Chapter III (2.8) in Macdonald's "Symmetric Functions and Hall Polynomials"

Published on 26 Mar 2026 - 22:16

score 55 · Answer 2 · 2021-03-07 18:27:11

55

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Need help with this induction proof

Published on 07 Mar 2021 - 18:27

score 249 · Answer 3 · 2021-03-14 01:44:44

249

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Inverse of a sixth order polynomial function

Published on 14 Mar 2021 - 1:44

score 81 · Answer 4 · 2021-04-02 19:29:21

81

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Integral Dependence of Symmetric functions (from Mumford's Red Book of Schemes)

Published on 02 Apr 2021 - 19:29

score 505 · Answer 5 · 2021-04-06 05:13:33

505

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The sum of $3$ real numbers is known to be zero. If the sum of their cubes is $e^{\pi}$ , what is their product equal to?

Published on 06 Apr 2021 - 5:13

score 92 · Answer 6 · 2021-04-10 14:23:38

92

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General formula for the sum of $k$-products

Published on 10 Apr 2021 - 14:23

score 106 · Answer 7 · 2021-04-12 22:38:45

106

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Evaluate $\sum_{r\in R^*}^{}{r^2}$ and prove that $R$ is a field

Published on 12 Apr 2021 - 22:38

score 142 · Answer 8 · 2021-04-13 23:00:59

142

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Identities similar to $\frac{a^3 + b^3 + c^3}{3} \cdot \frac{a^7 + b^7 + c^7}{7} = \left( \frac{a^5 + b^5 + c^5}{5} \right)^2$

Published on 13 Apr 2021 - 23:00

score 70 · Answer 9 · 2021-04-22 09:31:20

70

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Finding eigenvalues of Sym$^k(\varphi)$, with $\varphi$ an operator from an $n$-dimensional vector space $V$ to itself

Published on 22 Apr 2021 - 9:31

score 60 · Answer 10 · 2021-04-26 14:22:53

60

Views

Prime factors of power sum of roots

Published on 26 Apr 2021 - 14:22

score 103 · Answer 11 · 2026-03-27 14:58:27

103

Views

Schur-Positivity proof using Kashiwara crystals.

Published on 27 Mar 2026 - 14:58

score 63 · Answer 12 · 2021-04-29 10:21:23

63

Views

Choosing $m$ such that $x^p + mp^2 \left(x^{p-2} + \sum_1^{p-2} (-1)^i e_i x^{p-2-i} \right) -p$ has exactly $p-2$ real roots

Published on 29 Apr 2021 - 10:21

score 97 · Answer 13 · 2026-03-26 04:31:01

97

Views

Hall Scalar product calculation: $\langle h_3p_6, s_{(5,4)}\rangle$

Published on 26 Mar 2026 - 4:31

score 41 · Answer 14 · 2021-05-09 04:40:31

41

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Hilbert series for symmetric polynomial ring

Published on 09 May 2021 - 4:40

score 281 · Answer 15 · 2021-05-15 11:50:39

281

Views

Minimal Number of Polynomials to Determine a $2 \times 3$ Matrix up to Row Exchanges

Published on 15 May 2021 - 11:50

List Question

Hall-Littlewood polynomials and elementary symmetric functions-- Chapter III (2.8) in Macdonald's "Symmetric Functions and Hall Polynomials"

Need help with this induction proof

Inverse of a sixth order polynomial function

Integral Dependence of Symmetric functions (from Mumford's Red Book of Schemes)

The sum of $3$ real numbers is known to be zero. If the sum of their cubes is $e^{\pi}$ , what is their product equal to?

General formula for the sum of $k$-products

Evaluate $\sum_{r\in R^*}^{}{r^2}$ and prove that $R$ is a field

Identities similar to $\frac{a^3 + b^3 + c^3}{3} \cdot \frac{a^7 + b^7 + c^7}{7} = \left( \frac{a^5 + b^5 + c^5}{5} \right)^2$

Finding eigenvalues of Sym$^k(\varphi)$, with $\varphi$ an operator from an $n$-dimensional vector space $V$ to itself

Prime factors of power sum of roots

Schur-Positivity proof using Kashiwara crystals.

Choosing $m$ such that $x^p + mp^2 \left(x^{p-2} + \sum_1^{p-2} (-1)^i e_i x^{p-2-i} \right) -p$ has exactly $p-2$ real roots

Hall Scalar product calculation: $\langle h_3p_6, s_{(5,4)}\rangle$

Hilbert series for symmetric polynomial ring

Minimal Number of Polynomials to Determine a $2 \times 3$ Matrix up to Row Exchanges

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