Enumeration of Payphone Permutations

Abstract

The desire for privacy significantly impacts various aspects of social behavior as illustrated by people’s tendency to seek out the most secluded spot when multiple options are available. In particular, this can be seen at rows of payphones, where people tend to occupy an available payphone that is most distant from those already occupied. Assuming that there are n payphones in a row and that n people occupy payphones one after another as privately as possible, the resulting assignment of people to payphones defines a permutation, which we will refer to as a payphone permutation. In the present study, we consider different variations of payphone permutations and enumerate them.

MSC:

• 05A15
• 91F99

Acknowledgments

The author thanks Eli Bagno and anonymous reviewers for providing valuable comments on an earlier version of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Max A. Alekseyev

Max Alekseyev is an Associate Professor of mathematics and computational biology at the George Washington University. He holds M.S. in mathematics (1999) and Ph.D. in computer science (2007), and is a recipient of the CAREER award (2013) from the National Science Foundation and the John Riordan prize (2015) from the OEIS Foundation. His research interests range from discrete mathematics (particularly, combinatorics and graph theory) to computational biology (particularly, comparative genomics and genome assembly). He is a Senior Member of the ISCB and IEEE societies, and an Editor-in-Chief of the Online Encyclopedia of Integer Sequences.