Matroids Over One-Dimensional Groups. (24th July 2020) - Bollen, Guus P; Cartwright, Dustin; Draisma, Jan
Abstract: We develop the theory of matroids over one-dimensional algebraic groups, with special emphasis on positive characteristic. In particular, we compute the Lindström valuations and Frobenius flocks of such matroids. Building on work by Evans and Hrushovski, we show that the class of algebraic matroids, paired with their Lindström valuations, is not closed under duality of valuated matroids.