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symmetric polynomials indexed by the partition of zero

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#representation-theory #symmetric-groups #symmetric-polynomials
185
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Solve this system of equations for the value of $a,b$ and $c$ such that $a^3+3ab^2+3ac^2-6abc=1$,$b^3+3ba^2+3bc^2-6abc=1$,$c^3+3cb^2+3ca^2-6abc=1$

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#systems-of-equations #symmetric-polynomials
107
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An inequality with a condition

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#inequality #substitution #symmetric-polynomials #uvw #muirhead-inequality
488
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Prove that $3\left(\frac{x}{y} + \frac{y}{z} + \frac{z}{x}\right) \geq 2(x + y + z)\left (\frac{1}{y + z} + \frac{1}{x + z} + \frac{1}{x + y}\right)$

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#inequality #symmetric-polynomials #a.m.-g.m.-inequality #cauchy-schwarz-inequality #sum-of-squares-method
301
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Galois group of the general (indeterminate) polynomial equation

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#abstract-algebra #field-theory #galois-theory #symmetric-polynomials
158
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Resultant of Two Polynomials (D&F 14.6.31)

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#abstract-algebra #field-theory #symmetric-polynomials
56
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Decomposition of even symmetric polynomials and Euler numbers

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#combinatorics #permutations #symmetric-polynomials
218
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How to prove the case of equality in Schur's inequality?

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#combinatorics #inequality #symmetric-polynomials
77
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Prove that L is a positive symmetric operator

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#ordinary-differential-equations #operator-theory #symmetric-polynomials
172
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Prove $\sum\limits_{cyc}\frac{1}{x^{2017}+ x^{2015}+ 1} \geq 1$ with $x,\,y,\,z>0,\,xyz= 1$

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#inequality #symmetric-polynomials #jensen-inequality #muirhead-inequality
108
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Solution to polynomial equation

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#symmetric-polynomials #groebner-basis
65
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How to show that power sums determines ${x_1,...,x_n}$

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#polynomials #symmetric-polynomials
72
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Remainder of trinomial

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#divisibility #symmetric-polynomials #chinese-remainder-theorem
114
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Problem inequality

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#inequality #summation #symmetric-polynomials #a.m.-g.m.-inequality
61
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System of $4$ equations in three variables.

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#systems-of-equations #quadratics #symmetric-polynomials

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