Yeonkyung Kim - A Parking Function Setting for Nabla Images of Schur Functions

dmtcs:2361 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2361
A Parking Function Setting for Nabla Images of Schur FunctionsArticle

Authors: Yeonkyung Kim 1

  • 1 Department of Mathematics [Univ California San Diego]

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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Parking Function,Nabla,Hall-Littlewood operators,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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