Arithmetic partition sums and orbits of Z_n^k under the symmetric group S_k

Matthias Beck, Alex J. Feingold, Michael D. Weiner

We study M(n,k,r), the number of orbits of {(a_1,...,a_k)\in Z_n^k | a_1+...+a_k = r (mod n)} under the action of S_k. Equivalently, M(n,k,r) sums the partition numbers of an arith…