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Foundations of matroids. Part 1, Matroids without large uniform minors / Matthew Baker, Oliver Lorscheid

By: Contributor(s): Resource type: Ressourcentyp: BuchBookLanguage: English Series: American Mathematical Society. Memoirs of the American Mathematical Society ; volume 305, number 1536 (January 2025)Set: Foundations of matroids.Publisher: Providence, RI : American Mathematical Society, January 2025Description: v, 84 Seiten : IllustrationenISBN:
  • 9781470472689
Subject(s): Additional physical formats: Erscheint auch als: Foundations of matroids, Part 1. Online-Ausgabe Providence, RI : American Mathematical Society, 2025. 1 Online-Ressource (v, 84 Seiten)MSC: MSC: 05B35 | 20AxxRVK: RVK: SI 130Summary: The foundation of a matroid is a canonical algebraic invariant which classifies, in a certain precise sense, all representations of the matroid up to rescaling equivalence. Foundations of matroids are pastures, a simultaneous generalization of partial fields and hyperfields which are special cases of both tracts (as defined by the first author and Bowler) and ordered blue fields (as defined by the second author). Using deep results due to Tutte, Dress–Wenzel, and Gelfand–Rybnikov–Stone, we give a presentation for the foundation of a matroid in terms of generators and relations. The generators are certain “cross-ratios” generalizing the cross-ratio of four points on a projective line, and the relations encode dependencies between cross-ratios in certain low-rank configurations arising in projective geometry. Although the presentation of the foundation is valid for all matroids, it is simplest to apply in the case of matroids without large uniform minors. i.e., matroids having no minor corresponding to five points on a line or its dual configuration. For such matroids, we obtain a complete classification of all possible foundations.PPN: PPN: 1918877335
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Item type Home library Shelving location Call number Status
Institutsbestand Fachbibliothek Mathematik Bibliothek / frei aufgestellt Z 57 c-305.2025,1536 Nicht ausleihbar
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