The Arc Unknotting Game

Abstract

Summary Who doesn’t like games? And when games can involve interesting, visual, mathematical objects like knot diagrams, all the better! In this paper, we propose a new 2-player game on knot diagrams, the Arc Unknotting Game, that uses hot-off-the-press insights about the structure of knots. This game differs from previously studied games on knot diagrams—it’s much more slippery, with available moves appearing and disappearing in perplexing ways throughout the game. Intrigued? Then come play with us!