An Experimental Mathematics Approach to the Area Statistic of Parking Functions

TL;DR

This paper demonstrates an empirical approach to mathematical research using parking functions and their area statistic, emphasizing the rigor and effectiveness of finitistic, elementary methods supported by computational tools.

Contribution

It introduces a purely finitistic, elementary experimental methodology for studying parking functions, showcasing its rigor and utility in combinatorial mathematics.

Findings

Validated empirical methods for analyzing parking functions

Demonstrated the effectiveness of computational tools in combinatorics

Provided new insights into the area statistic of parking functions

Abstract

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.