Paper
Zero-sum multisets mod p with an application to surface automorphisms
Authors
Anthony Weaver
Abstract
We solve a problem in enumerative combinatorics which is equivalent to counting topological types of certain group actions on compact Riemann surfaces. Let be the two-dimensional vector space over , the field with elements, an odd prime. We count orbits of the general linear group on certain multisets consisting of non-zero columns from . The -multisets are `zero-sum,' that is, the sum (mod ) over the columns in the multiset is . The orbit count yields the number of topological types of fully ramified actions of the elementary abelian -group of rank on compact Riemann surfaces of genus