Large-scale Monte Carlo simulations for zeros in character tables of symmetric groups

This is a brief report on some recent large-scale Monte Carlo simulations for approximating the density of zeros in character tables of large symmetric groups. Previous computations suggested that a large fraction of zeros cannot be explained by classical vanishing results. Our computations eclipse previous ones and suggest that the opposite is true. In fact, we find empirically that almost all of the zeros are of a single classical type.