Partitions of the complete hypergraph K-6(3) and a determinant-like function

摘要

In this paper, we introduce a determinant-like map det(S3) and study some of its properties. For this, we define a graded vector space Lambda(S3)(V) that has similar properties with the exterior algebra Lambda(V) and the exterior GSC-operad Lambda(S2)(V) from Staic. When dim(V-2) = 2, we show that dim(k)(Lambda(S3)(V2) 6) = 1, which gives the existence and uniqueness of the map det(S3). We also give an explicit formula for det(S3) as a sum over certain 2-partitions of the complete hypergraph K-6(3).