Using limit linear series and a result controlling degeneration from separable maps to inseparable maps, we give a formula for the number of rational functions (up to automor-phism of the target) on the projective line with ramification to order e i at general points P i , in the case that all e i are less than the characteristic. Unlike the case of characteristic 0, the answer is not given by
... [Show full abstract] Schubert calculus, nor is the number of maps always finite for distinct P i , even in the tamely ramified case. However, finiteness for general P i , obtained by exploiting the relationship to branched covers, is a key part of the argument.