First Written: April 25, 2018

Maple packages

• ParkingAndTrees.txt, a Maple package with TWO bijections between forests of rooted trees and a-parking functions

• ParkingStatistics.txt, a Maple package with TWO bijections between forests of rooted trees and a-parking functions

Sample Input and Output for ParkingAndTrees.txt

• If you want to see the images under the First (recursive-style) bijection for all (usual, i.e. 1-) parking functions of size up to 5

  the input file generates the output file.

Sample Input and Output for ParkingStatistics.txt

• If you want to see the first 70 terms of the sequence of weight-enumerators for parking functions, according to the sum, and the statistical information for those between 60 and 70,

  the input file generates the output file.

• If you want to statistical information about the random variable "sum of the parking function" and the statistical information for those between 121 and 130,

  the input file generates the output file.

• If you want to see EXPLICIT expressions for the second through seventh moments about the mean, in terms of n and the Expectation of the random variable "sum of the parking function"

  the input file generates the output file.

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