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.
Domains
Discrete Mathematics [cs.DM]
Origin : Publisher files allowed on an open archive
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