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Results tagged with symmetric-functions
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user 115255
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.
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On two types of shifted symmetric power sums
In the ring of shifted symmetric functions $\Lambda^*$ there are many ways to generalize the symmetric power sums. First of all, we have the functions $$p^*_k=\sum_{i=1} \left((x_i-i+1/2)^k-(-i+1/2)^k …
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On two types of shifted symmetric power sums
The answer to this question is precisely given by the Gromov-Witten/Hurwitz correspondence by Okounkov and Pandharipande (see https://arxiv.org/abs/math/0204305). Up to the constant $(1-2^{-k})\zeta(- …