I will introduce an incidence-based orientation scheme for hypergraphs that combinatorially models {0, +1, −1}-matrices. I will discuss the problem of translation versus extension of graph theoretic concepts to hypergraphic ones. I will introduce new hypergraphic structures and operations, with an emphasis on their relation to the classification of the minimal column dependencies of {0, +1, −1}-matrices.
I will discuss the notion of "balance" in oriented hypergraphs and complete the collection of oriented hypergraphic concepts related to the classification of the minimal dependencies of {0, +1, −1}-matrices. Topics covered will include the decomposition of oriented hypergraphs into three families of varying degrees of "balance", a discussion of the classification of the minimal dependencies of two of these families, and, if time permits, various open problems surrounding the remaining family.