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- W3037161520 abstract "We explore a combinatorial theory of linear dependency in space, complex with foundations analogous to those for oriented matroids. We give multiple equivalent axiomatizations of matroids, showing that this theory captures properties of linear dependency, orthogonality, and determinants over C in much the same way that oriented matroids capture the same properties over R. In addition, our matroids come with a canonical circle action analogous to the action of C* on a vector space. Our phirotopes (analogues of determinants) are the same as those studied previously by Below, Krummeck, and Richter-Gebert and by Delucchi. We further show that matroids cannot have vector axioms analogous to those for oriented matroids." @default.
- W3037161520 created "2020-07-02" @default.
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- W3037161520 date "2010-05-19" @default.
- W3037161520 modified "2023-09-26" @default.
- W3037161520 title "Complex Matroids" @default.
- W3037161520 hasPublicationYear "2010" @default.
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