Exact results at the two-dimensional percolation point

We derive exact expressions for the excess number of clusters b and the excess cumulants bₙ of a related quantity at the two-dimensional percolation point. High-accuracy computer simulations are in accord with our predictions. The parameter b is a finite-size correction to the Temperley-Lieb or Baxter-Temperley-Ashley formula for the number of clusters per site nc in the infinite system limit; the bₙ correct bulk cumulants. Both b and bₙ are universal, and thus depend only on the system's shape. Higher-order corrections show no apparent dependence on fractional powers of the system size.