Written: Feb. 17, 2023

[To appear in the Palestinian Journal of Mathematics]

Maple package

• SMCboole.txt, a Maple package for computing explicit expressions, in n, for moments of r.v. "number of k-dim subcubes" in the (truth table) of a (uniformly) random Boolean function.

Sample Input and Output for SMCboole.txt

• If you want to see the third through the sixth moments (about the mean), and the scaled versions, as explicit expressions in n, for the random variable "number of edges contained in the truth-table of a random Boolean function of n variables"
  the input gives the output.

• If you want to see the third and fourth moments (about the mean), and the scaled versions, as explicit expressions in n, for the random variable "number of squares (i.e. two-dimensional unit cubes) contained in the truth-table of a random Boolean function of n variables"
  the input gives the output.

• If you want to see the third moment (about the mean), and the scaled version, as an explicit expression in n, for the random variable "number of 3-dim cubes contained in the truth-table of a random Boolean function of n variables"
  the input gives the output.

Coefficients for the correlation of X_r and X_s can be found in this file

Mathematical Works by Svante Janson

Blair Seidler's homepage

Papers by Doron Zeilberger.