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A Shifted Parking Function Symmetric Function

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arxiv 2405.02164 v1 pith:IWE63XPP submitted 2024-05-03 math.CO

Richard P. Stanley This is my paper · ORCID
classification math.CO
keywords functionshiftedanaloguemathrmparkingsymmetricfunctionsbases
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abstract

We define a "shifted analogue" $\mathrm{SH}_n$ of the parking function symmetric function $\mathrm{PF}_n$. The expansion of $\mathrm{SH}_n$ in terms of three bases for shifted symmetric functions is explicitly described. We don't know a shifted analogue for parking functions themselves, but some desirable properties of such an analogue are discussed.

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  1. Odd Shifted Parking Functions

    math.CO 2025-05 reject novelty 8.0 of 10

    Odd shifted parking functions are defined and claimed to recover SH_n via V_{shape(p)}, resolving Stanley's open problem, but the proof has a gap.

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