English

The Absent-Minded Passengers Problem via Computer Algebra

Combinatorics 2020-01-22 v1 Probability

Abstract

In a delightful article that recently appeared in the American Mathematics Monthly, Norbert Henze and Guenter Last discuss the "Absent-Minded Passengers" Problem, but left open finding an explicit expression for the probability generating function, of the random variable "Number of passengers occupying a wrong seat", when the number of absent-minded passengers is larger than one. This is accomplished in this note, using experimental mathematics and symbolic computation. We also derive explicit expressions for the first 8 moments of the original case of one absent-minded passenger, and indicate how to extend it to the general case

Cite

@article{arxiv.2001.06839,
  title  = {The Absent-Minded Passengers Problem via Computer Algebra},
  author = {Shalosh B. Ekhad and Doron Zeilberger},
  journal= {arXiv preprint arXiv:2001.06839},
  year   = {2020}
}

Comments

7 pages; Accompanied by a Maple package available from https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/amp.html

R2 v1 2026-06-23T13:15:02.700Z