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arXiv · 2412.11222

A Short Proof that the number of $(a,b)$-parking functions of length n $a(a+bn)^{n-1}$

AJ Bu·Doron Zeilberger
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Abstract

We give a very short proof of the fact that the number of $(a,b)$-parking functions of length $n$ equals $a(a+bn)^{n-1}$. This was first proved in 2003 by Kung and Yan, via a very long and torturous route, as a corollary of a more general result. This new version contains a reference to previous work kindly communicated by Richard Stanley

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AJ Bu, Doron Zeilberger. 2024-12-21. A Short Proof that the number of $(a,b)$-parking functions of length n $a(a+bn)^{n-1}$. https://arxiv.org/abs/2412.11222

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