Corner contribution to percolation cluster numbers

We study the number of clusters in two-dimensional (2d) critical percolation, N_Γ, which intersect a given subset of bonds, Γ. In the simplest case, when Γ is a simple closed curve, N _Γ is related to the entanglement entropy of the critical diluted quantum Ising model, in which Γ represents the boundary between the subsystem and the environment. Due to corners in Γ there are universal logarithmic corrections to N_Γ, which are calculated in the continuum limit through conformal invariance, making use of the Cardy-Peschel formula. The exact formulas are confirmed by large-scale Monte Carlo simulations. These results are extended to anisotropic percolation where they confirm a result of discrete holomorphicity.