Oriented hypergraphs: Balanceability

An oriented hypergraph is an incidence structure that extends the concepts of signed graphs, balanced hypergraphs, and matrices. We introduce hypergraphic structures techniques generalize circuit classification graphic frame matroid to any matrix via its locally-signed-graphic substructure. To achieve this, Camion's algorithm applied hypergraphs provide a generalization reorientation sets frustration only well-defined on balanceable hypergraphs. A simple partial characterization unbalanceable circuits applications representable matroids demonstrating difference between Fano non-Fano one balance.