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The Stanley Conjecture Revisited
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The Stanley Conjecture Revisited
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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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Cited by 1 Pith paper
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Hidden Structure of Jack Littlewood-Richardson Coefficients
Jack LR coefficients g_μν^λ(α) arise as specializations of novel polynomials that are invariant under S6 x Z2 for (21,21,321) and conjecturally factor on hyperplanes due to Young-graph compatibility.
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