Exact results for average cluster numbers in bond percolation on infinite-length lattice strips

We calculate exact analytic expressions for the average cluster numbers 〈k〉_{Λ_{s}} on infinite-length strips Λ_{s}, with various widths, of several different lattices, as functions of the bond occupation probability p. It is proved that these expressions are rational functions of p. As special cases of our results, we obtain exact values of 〈k〉_{Λ_{s}} and derivatives of 〈k〉_{Λ_{s}} with respect to p, evaluated at the critical percolation...