Partitions of the complete hypergraph K₆³ and a determinant like function

2021/07/28 by Steven R. Lippold, Lippold, Steven R., Mihai D. Staic +1
Mathematics · #05C70 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Primary 15A15 #Rings and Algebras (math.RA) #Secondary 05C65 #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2107.13609

openalex publication_date 2021/07/28 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

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 Λ^S3_V that has similar properties with the exterior algebra Λ_V and the exterior GSC-operad Λ^S2_V from \citesta2. When dim(V₂)=2 we show that dim_k(Λ^S3_V2[6])=1 which gives the existence and uniqueness of det^S3. We also give an explicit formula for det^S3 as a sum over certain 2-partitions of the complete hypergraph K₆³.

Related

• Edge partitions of the complete graph and a determinant like function
• Introduction to the hyperdeterminant and to the rank of multidimensional matrices
• Lower bounds on the strength of the determinant
• Determinantal hypersurfaces
• Partitions of single exterior type