A Model for Pairs of Beatty Sequences

TL;DR

This paper explores the properties of pairs of Beatty sequences generated by athletes running in opposite directions, providing insights into their partitioning behavior of integers based on initial conditions.

Contribution

It offers a new interpretation of partitioning criteria for Beatty sequences through a physical analogy involving athletes in a stadium.

Findings

Sequences partition integers when athletes start at the same point

Physical analogy clarifies mathematical partitioning conditions

Results connect sequence properties with initial conditions

Abstract

Two Beatty sequences are recorded by athletes running in opposite directions in a round stadium. This approach suggests a nice interpretation for well known partitioning criteria: such sequences (eventually) partition the integers essentially when the athletes have the same starting point.