Chess Billiards

TL;DR

This paper demonstrates that the chess billiard map is a circle homeomorphism, surveys related circle homeomorphism results, and provides new insights addressing open questions from prior work.

Contribution

It establishes the chess billiard map as a circle homeomorphism and applies existing theory to derive new results solving open problems.

Findings

Chess billiard map is a circle homeomorphism

New results answer open questions from previous research

Application of circle homeomorphism theory to chess problems

Abstract

We show the chess billiard map, which was introduced in [HM] in order to study a generalization of the $n$-Queens problem in chess, is a circle homeomorphism. We give a survey of some of the known results on circle homeomorphisms, and apply them to this map. We prove a number of new results which give answers to some of the open questions posed in [HM].