Tagged Questions
1
vote
1answer
49 views
Decomposition of products of monomial symmetric polynomials into sums of them
I'm trying to make sense of the answer given in: this question
I am stuck at the phrase 'where the partitions $\gamma$ result from adding, respectively, from $\alpha$ all distinct partitions obtained ...
2
votes
0answers
57 views
Reference request on symmetric polynomials
Let $e_k$ be the $k$th-degree elementary symmetric polynomial in $x_1,\ldots,x_n$ (and recall that $e_k=0$ if $k>n$).
I know very little about these polynomials. I've just noticed this odd ...
3
votes
0answers
40 views
Symmetrizing a sequence of vectors
Given a finite set of real numbers $X_1, \ldots, X_n$, we can compute the first $n$ power sums of these numbers. From the power sums, the set $\{X_1, \ldots, X_n\}$ can be recovered. Essentially we ...
2
votes
1answer
103 views
Primitive Element for Field Extension of Rational Functions over Symmetric Rational Functions
A rational function $f$ in $n$ variables is a ratio of $2$ polynomials,
$$f(x_1,...x_n) = \frac{p(x_1,...x_n)}{q(x_1,...x_n)}$$
where $q$ is not identically $0$. The function is called symmetric if ...
9
votes
1answer
150 views
What are the analogues of Littlewood-Richardson coefficients for monomial symmetric polynomials?
The product of monomial symmetric polynomials can be expressed as
$m_{\lambda} m_{\mu} = \Sigma c_{\lambda\mu}^{\nu}m_{\nu}$
for some constants $c_{\lambda\mu}^{\nu}$.
In the case of Schur ...
5
votes
0answers
96 views
Schur skew functions
Let $\lambda,\mu,\nu$ be some partitions. Let's denote with $s_\lambda,s_\mu,s_\nu$ the Schur functions associated to these partitions. If
$s_\mu s_\nu=\sum_\lambda c^\lambda_{\mu\nu}s_\lambda$
...
4
votes
2answers
433 views
Sum of cubed roots
I need to calculate the sums
$$x_1^3 + x_2^3 + x_3^3$$
and
$$x_1^4 + x_2^4 + x_3^4$$
where $x_1, x_2, x_3$ are the roots of
$$x^3+2x^2+3x+4=0$$
using Viete's formulas.
I know that ...
