An Experimental Mathematics Approach to the Area Statistic of Parking Functions

By Yukun Yao and Doron Zeilberger

.pdf   .ps   .tex
Version with pictures: .pdf   LaTeX  

[Appeared in Mathematical Intelligencer volume 41, issue 2 (June 2019), pp. 1-8]

First Written: June 5, 2018; This version: Aug. 29, 2018.

Last update of this web-page (but not the article): Jan. 15, 2019.

We illustrate the experimental, empirical, approach to mathematics (that contrary to popular belief, is often rigorous), by using parking functions and their "area" statistic, as a case study. Our methods are purely finitistic and elementary, taking full advantage, of course, of our beloved silicon servants.

Maple package

Pictures produced by ParkingStatistics.txt

Sample Input and Output for ParkingStatistics.txt

Added Jan. 15, 2019: Yukun Yao and myself I giving a talk at the JMM on Jan. 19, 2019. Since we will mention briefly Henry Pollack's clever proof, I have written a short Maple package to experiment with it. The Maple package is ParkingPollack.txt and

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