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arXiv · 2401.01582

The Stanley Conjecture Revisited

Ryan Mickler
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Abstract

In the seminal work of Stanley, several conjectures were made on the structure of Littlewood-Richardson coefficients for the multiplication of Jack symmetric functions. Motivated by recent results of Alexandersson and the present author, we postulate that a `windowing' property holds for all such Jack L-R coefficients. Furthermore, we propose an extension of the `Factorization' property for Schur L-R due to King-Tollu-Toumazet to the Jack case. These properties provide a vast set of relations between the Jack L-R coefficients and allow for their direct computation in a certain large class of cases.

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Ryan Mickler. 2025-07-20. The Stanley Conjecture Revisited. https://arxiv.org/abs/2401.01582

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