Combinatorial enumeration of cyclic covers of P1

Abstract

We study plane algebraic curves defined over a field k of arbitrary characteristic that are ramified coveringsof the projective line $P1(k)$ branched over a given configuration of distinct points by their ramification type specifiedby a partition of d the degree of the covering. We enumerate them by using the combinatorics of partitions and itsconnection to the representation theory of the symmetric group.