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arXiv · 2107.13609

Partitions of the complete hypergraph $K_6^3$ and a determinant like function

Steven R. Lippold·Mihai D. Staic
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Abstract

In this paper we introduce a determinant-like map $det^{S^3}$ and study some of its properties. For this we define a graded vector space $Λ^{S^3}_V$ that has similar properties with the exterior algebra $Λ_V$ and the exterior GSC-operad $Λ^{S^2}_V$ from \cite{sta2}. When $dim(V_2)=2$ we show that $dim_k(Λ^{S^3}_{V_2}[6])=1$ which gives the existence and uniqueness of $det^{S^3}$. We also give an explicit formula for $det^{S^3}$ as a sum over certain $2$-partitions of the complete hypergraph $K_6^3$.

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Steven R. Lippold, Mihai D. Staic. 2021-07-28. Partitions of the complete hypergraph $K_6^3$ and a determinant like function. https://arxiv.org/abs/2107.13609

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