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.
A Shifted Parking Function Symmetric Function
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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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math.CO 1years
2025 1verdicts
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Odd Shifted Parking Functions
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.