Anderson: vectors of matroids over tracts

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Laura Anderson, "Vectors of matroids over tracts," arXiv:1607.04868 (2016).

This paper develops vector and covector theories for matroids over tracts, a framework encompassing ordinary fields, partial fields, and hyperfields such as the sign hyperfield. It relates vectors and covectors to circuits and cocircuits through orthogonality, and shows that the Composition and Elimination axioms for vectors of oriented matroids, and some duality and minor properties, fail for general tracts.' Replace 'Held copy and library card' with 'Library card

The possible value for E0774 is conceptual: dissociation is sensitive to the sign pattern and coefficient restriction of a relation, so an ordinary matroid forgets too much. A tract-valued model might retain the missing signed data and clarify whether an Edmonds-type partition principle can survive. The paper does not directly model the hard coefficient cutoff $\{0,\pm1\}$, so any claimed application must specify the tract and prove that its independent sets coincide with dissociated subsets.