# Questions tagged [symmetric-functions]

For questions about functions which are symmetric in their arguments.

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### Largest normal distribution under a curve

I was wondering if I could have some insights on the following problem. Suppose I have a probability distribution $F$, I want an algorithm that finds the largest normal distribution under $F$. Say we ...
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### Building the tensor product of multiple algebras in sage?

I want to build $\Lambda\otimes\Lambda$ in Sage, where $\Lambda$ is the algebra of symmetric functions. You can build the algebra of symmetric functions in the Schur bases with SymmetricFunctions(QQ)....
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• 1,219
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### Prove that $n$ hypersurfaces with cyclic permutations of the last $n-1$ variables only intersect if all the variables have the same value.

Suppose that in $\mathbb{R}^n$, I have an equation $F(x,y,z,\dots,n)=0$ with the property that it is symmetric in the last $(n-1)$ variables $\{y,z,\dots,n\}$, but not in the first variable $x$. For ...
• 169
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### Symmetric PDFs for random sets

I’m studying the probability theory for finite sets (in my field we call them Random Finite Sets, but they are known as (simple) Point Processes). In this context, a random finite set is a random ...
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### Symmetric sigmoidal function with asymptotes?

Consider the cubic function: f(x) = x + ax^3 Simple cubic function This function has several of the features that I need, which are: crosses the origin (0,0) If x > 0 then y <= x If x < 0 ...
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1 vote
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### Plethysm Substitution Rule issue

I am looking at the plethysm "negation rule," Theorem 6 If $g\in\Lambda^n$ is homogeneous of degree $n$ and $A$ is any plethystic alphabet, then $$g[-A]=(-1)^n\big(\omega(g)\big)[A].$$ In ...
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1 vote
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### Does this 3D function need to be symmetric for $\frac {\partial f(x,y)}{\partial x}= |\frac {\partial f(x,y)}{\partial y}|$ for all $x < y$?

Suppose I have a 3D function $f(x,y):\mathbb {R^2_{\ge 0}} \to \mathbb {R_{\le0}}$ such that  \frac {\partial f(x,y)}{\partial x}= \begin{cases} >0&\text{if}\, x<y \\\ 0&\text{if}\, ...
• 61
1 vote
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### Filling in the gap of a proof of the Fundamental Theorem of Symmetric Polynomials.

Suppose we can assume that the set of symmetric rational functions in $k(X_1,...,X_n)$, where $k$ is a field, is the same as the field generated by $k(a_1,...,a_n)$ where the $a_i$ are the elementary ...
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1 vote
### Image of permutations $\lambda$ with $l(\lambda) \leq 2$ under RSK
Consider $p,q \in SSYT(\lambda)$ such that $l(p) = l(q) \leq 2$. I was hoping to find the image under the rsk algorithm of $(p,q)$? In other words the two lines-arrays (or generalized permutations) ...