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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.15680 |
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Table of Contents:
- We consider polynomials of the form $\operatorname{s}_λ(y_1^{[\varkappa_1]},\ldots,y_n^{[\varkappa_n]})$, where $λ$ is an integer partition, $\operatorname{s}_λ$ is the Schur polynomial associated to $λ$, and $y_j^{[\varkappa_j]}$ denotes $y_j$ repeated $\varkappa_j$ times. We represent $\operatorname{s}_λ(y_1^{[\varkappa_1]},\ldots,y_n^{[\varkappa_n]})$ as a quotient whose the denominator is the determinant of the confluent Vandermonde matrix, and the numerator is the determinant of some generalized confluent Vandermonde matrix. We give three algebraic proofs of this formula.