Anderson, Laura and Delucchi, Emanuele (2012) Foundations for a Theory of Complex Matroids. Discrete & Computational Geometry. ISSN 0179-5376
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We explore a combinatorial theory of linear dependency in complex space, complex matroids, with foundations analogous to those for oriented matroids. We give multiple equivalent axiomatizations of complex 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 complex matroids come with a canonical circle action analogous to the action of C* on a complex vector space. Our phirotopes (analogs of determinants) are the same as those studied previously by Below, Krummeck, and Richter-Gebert (Discrete and Computational Geometry, Springer, pp. 203–233, 2003) and Delucchi (Diploma Thesis, ETH Zurich, 2003). We further show that complex matroids cannot have vector axioms analogous to those for oriented matroids.
| Item Type: | Scientific journal article, Newspaper article or Magazine article |
|---|---|
| Subjects: | Mathematical sciences |
| Department/unit: | Dipartimento tecnologie innovative > Istituto Dalle Molle di studi sull'intelligenza artificiale |
| Depositing User: | Emanuele Delucchi |
| Date Deposited: | 07 Jun 2022 09:18 |
| Last Modified: | 07 Jun 2022 09:22 |
| URI: | http://repository.supsi.ch/id/eprint/13414 |
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