https://orcid.org/0000-0001-5675-8484
Summary
For a lifeguard at a crowded city pool, rotating from station to station, those periodic fifteen-minute breaks between stations are precious commodities. Moreover, since these breaks provide some rare quality time with the other break guards, a lifeguard’s question is this: given a certain rotation consisting of stations and breaks, how many of one’s breaks are shared with each coworker? Abstract algebra comes to the rescue: we show how the answer, for all coworkers art once, can be packaged in a generating function, computed by an easy calculation in the group ring of the cyclic group.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Notes on contributors
William Q. Erickson
William Q. Erickson (MR Author ID: 1470622; ORCID: 0000-0001-5675-8484) is a postdoctoral research fellow with interests in the representation theory of Lie groups, invariant theory, combinatorics, and algebraic statistics. He would like to dedicate this math problem to the memory of Buchner Pool (1967–2020), and to all the lifeguards there who kept it safe and happy.