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Results tagged with symmetric-functions
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user 10881
Symmetric functions are symmetric polynomials, in finitely many, or countably infinitely many variables. They arise in the representation theory of symmetric groups and in the polynomial representation theory of general linear groups. Bases of the ring of symmetric functions are indexed by integer partitions. Schur functions, elementary symmetric functions, complete symmetric functions, and power sum symmetric functions are the most commonly used bases.
7
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2
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About the sum of rectangular power sums
Let $n \geq 1$ be an integer and consider the symmetric function
$$D_n = \sum_{d|n} p_d^{n/d},$$
where $p_{d}$ are the power-sum symmetric functions.
It can be checked up to $n=35$ that the symmetric …
- 3,597
7
votes
Symmetric powers of Schur polynomials
this could be done in sage:
sage: B3 = WeylCharacterRing("B3", style="coroots")
sage: spin = B3(0,0,1)
sage: spin.symmetric_power(6)
B3(0,0,0) + B3(0,0,2) + B3(0,0,4) + B3(0,0,6)
sage: A3 = WeylChar …
- 3,597
7
votes
Accepted
Super-plethysm?
This amounts to study composition of "linear species" in the category of complexes.
The correct way to handle these computations using plethysm is
to introduce an auxiliary variable $t$ and to weight …
- 3,597