Johannes Schmidt’s scientific contributions

We use transfer matrix methods to determine bounds for the numbers of legal Go positions for various numbers of players on some planar lattice graphs, including square lattice graphs such as those on which the game is normally played. We also Þnd bounds on limiting constants that describe the behaviour of the number of legal positions on these lattice graphs as the dimensions of the lattices tend to inÞnity. These results amount to giving bounds for some speciÞc evaluations of Go polynomials on these graphs.