Enumerating Seating Arrangements that Obey Social Distancing

Abstract

We study maximal seating arrangements, either on a line, or in a rectangular auditorium with a fixed number of columns but an arbitrary number of rows, that obey any prescribed set of `social distancing' restrictions. In addition to enumeration, we study the statistical distribution of the density, and give efficient algorithms for generating these at random

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