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Results tagged with symmetric-functions
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user 6771
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.
16
votes
Accepted
Is there a short proof that the Kostka number $K_{\lambda \mu}$ is non-zero whenever $\lambd...
I think the following is a simple combinatorial argument which constructs the most dominant semistandard $\lambda$-tableau of content $\mu$ whenever $\lambda\trianglerighteq\mu$. (n.b. I haven't foll …
- 1,570
4
votes
2
answers
278
views
Pieri-type rule for Schur P-functions
This question is about symmetric functions. As usual, let $s_\lambda$ denote the Schur function corresponding to a partition $\lambda$. For $r\geqslant1$, let $d_r$ denote the map defined on symmetric …
- 1,570