The numbers game and coxeter groups Original Research Article

The numbers game of Mozes, a combinatorial one-player game, is closely connected to Coxeter groups. This paper shows that the moves of a numbers game generates a Coxeter group and interprets the basic elements of the numbers game in terms of Coxeter group theory. In the ‘node weighted game’, a generalization of the numbers game, the moves are not involutions, and therefore do not generate a Coxeter group. However, surprisingly many of the seemingly Coxeter group dependent results carry over from the ordinary numbers game. A proof based on these results shows that the language of legal play is a greedoid.