A note on the λλ-structure on the Burnside ring

Let GG be a finite group and let SS be a GG-set. The Burnside ring of GG has a natural structure of a λλ-ring, {λn}n∈N{λn}n∈N. However, a priori λn(S)λn(S), where SS is a GG-set, can only be computed recursively, by first computing λ1(S),…,λn−1(S)λ1(S),…,λn−1(S). In this paper we establish an explicit formula, expressing λn(S)λn(S) as a linear combination of classes of GG-sets.