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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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Submitted on : Tuesday, November 17, 2015 - 10:20:08 AM
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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, ⟨10.46298/dmtcs.2361⟩. ⟨hal-01229698⟩



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