An Experimental Mathematics Approach to the Area Statistic of Parking Functions

By Yukun Yao and Doron Zeilberger

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[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): Dec. 11, 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.

Added Dec. 11, 2019: We just got the following message from guru Donald Knuth:

Hi Doron,

I enjoyed, as usual, your recent contribution to the Intelligencer.

Conversely, you might enjoy the discussion of these issues in Volume 3 of The Art of Computer Programming, in the answers to exercises 6.4--29ff on pages 732--734.

The footnote on page 536 also explains why this was, in a sense, the problem that originally got me hooked on analysis of algorithms in the first place!

Cordially, Don

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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