# program to compute hurwitz numbers

Is there a computer program available to compute Hurwitz numbers easily? In fact I only care about counting covers $$C\to\mathbb{P}^1$$ branched over $$0,1,\infty$$, and am even willing to restrict to the case $$C=\mathbb{P}^1$$.

In combinatorial language, I would like to input integers $$d\ge1,g\ge0$$ and three partitions $$\lambda_1,\lambda_2,\lambda_3$$ of $$d$$ such that the total number of parts of the $$\lambda_i$$ is $$d-2g+2$$, and compute, up to simultaneous conjugation, the (weighted) number of permutations $$\sigma_1,\sigma_2,\sigma_3\in S_d$$, where $$\sigma_i$$ has cycle type $$\lambda_i$$, for which the $$\sigma_i$$ generate a transitive subgroup of $$S_d$$ and $$\sigma_1\sigma_2\sigma_3=1$$.