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A Parking Function Setting for Nabla Images of Schur Functions

Abstract : In this article, we show how the compositional refinement of the ``Shuffle Conjecture'' due to Jim Haglund, Jennifer Morse, and Mike Zabrocki can be used to express the image of a Schur function under the Bergeron-Garsia Nabla operator as a weighted sum of a suitable collection of ``Parking Functions.'' The validity of these expressions is, of course, going to be conjectural until the compositional refinement of the Shuffle Conjecture is established.
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https://hal.inria.fr/hal-01229698
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Yeonkyung Kim. A Parking Function Setting for Nabla Images of Schur Functions. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.1005-1016. ⟨hal-01229698⟩

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