Foundations of Matroids:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence
American Mathematical Society
2025-
|
| Ausgabe: | Pt. 1.2025- |
| Schriftenreihe: | Memoirs of the American Mathematical Society Series
... |
| Abstract: | Cover -- Title page -- Introduction -- A quick introduction to pastures -- Representations of matroids over pastures and the foundation of a matroid -- Products and coproducts -- Universal cross ratios -- The structure theorem for foundations of matroids without large uniform minors -- Consequences of the structure theorem -- Content overview -- Acknowledgments -- Chapter 1. Background -- 1.1. Notation -- 1.2. The Tutte group -- 1.3. Embedded minors -- Chapter 2. Pastures -- 2.1. Definition and first properties -- 2.2. Matroid representations -- 2.3. Matroid representations via hyperplane functions -- 2.4. The universal pasture -- 2.5. The Tutte group and the universal pasture -- Chapter 3. Cross ratios -- 3.1. Cross ratios of -matroids -- 3.2. Cross ratios for hyperplanes -- 3.3. Universal cross ratios -- 3.4. Fundamental elements -- 3.5. Compatibility with the Tutte group formulation of Dress and Wenzel -- Chapter 4. Foundations -- 4.1. Definition and basic facts -- 4.2. Universal cross ratios as generators of the foundation -- 4.3. The foundation of the dual matroid -- 4.4. Foundations of embedded minors -- 4.5. The foundation of ²₄ -- 4.6. The tip and cotip relations -- 4.7. Relations for parallel elements -- 4.8. The foundation of the Fano matroid and its dual -- 4.9. A presentation of the foundation by hyperplanes -- 4.10. A presentation of the foundation by bases -- 4.11. A presentation of the foundation by embedded minors -- Chapter 5. The structure theorem -- 5.1. Foundations of matroids on 5 elements -- 5.2. Symmetry quotients -- 5.3. The structure theorem for matroids without large uniform minors -- Chapter 6. Applications -- 6.1. Forbidden minors for regular, binary and ternary matroids -- 6.2. Uniqueness of the rescaling class over F₃ -- 6.3. Criteria for representability over certain fields. |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
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| 100 | 1 | |a Baker, Matthew |d 1973- |e Verfasser |0 (DE-588)136700748 |4 aut | |
| 245 | 1 | 0 | |a Foundations of Matroids |
| 250 | |a Pt. 1.2025- | ||
| 264 | 1 | |a Providence |b American Mathematical Society |c 2025- | |
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| 490 | 0 | |a Memoirs of the American Mathematical Society Series |v ... | |
| 500 | |a Description based on publisher supplied metadata and other sources | ||
| 520 | 3 | |a Cover -- Title page -- Introduction -- A quick introduction to pastures -- Representations of matroids over pastures and the foundation of a matroid -- Products and coproducts -- Universal cross ratios -- The structure theorem for foundations of matroids without large uniform minors -- Consequences of the structure theorem -- Content overview -- Acknowledgments -- Chapter 1. Background -- 1.1. Notation -- 1.2. The Tutte group -- 1.3. Embedded minors -- Chapter 2. Pastures -- 2.1. Definition and first properties -- 2.2. Matroid representations -- 2.3. Matroid representations via hyperplane functions -- 2.4. The universal pasture -- 2.5. The Tutte group and the universal pasture -- Chapter 3. Cross ratios -- 3.1. Cross ratios of -matroids -- 3.2. Cross ratios for hyperplanes -- 3.3. Universal cross ratios -- 3.4. Fundamental elements -- 3.5. Compatibility with the Tutte group formulation of Dress and Wenzel -- Chapter 4. Foundations -- 4.1. Definition and basic facts -- 4.2. Universal cross ratios as generators of the foundation -- 4.3. The foundation of the dual matroid -- 4.4. Foundations of embedded minors -- 4.5. The foundation of ²₄ -- 4.6. The tip and cotip relations -- 4.7. Relations for parallel elements -- 4.8. The foundation of the Fano matroid and its dual -- 4.9. A presentation of the foundation by hyperplanes -- 4.10. A presentation of the foundation by bases -- 4.11. A presentation of the foundation by embedded minors -- Chapter 5. The structure theorem -- 5.1. Foundations of matroids on 5 elements -- 5.2. Symmetry quotients -- 5.3. The structure theorem for matroids without large uniform minors -- Chapter 6. Applications -- 6.1. Forbidden minors for regular, binary and ternary matroids -- 6.2. Uniqueness of the rescaling class over F₃ -- 6.3. Criteria for representability over certain fields. | |
| 700 | 1 | |a Lorscheid, Oliver |d 1978- |e Verfasser |0 (DE-588)1201611245 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-035507203 | |
Datensatz im Suchindex
| _version_ | 1824385133533200385 |
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| author | Baker, Matthew 1973- Lorscheid, Oliver 1978- |
| author_GND | (DE-588)136700748 (DE-588)1201611245 |
| author_facet | Baker, Matthew 1973- Lorscheid, Oliver 1978- |
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| author_sort | Baker, Matthew 1973- |
| author_variant | m b mb o l ol |
| building | Verbundindex |
| bvnumber | BV050171277 |
| ctrlnum | (DE-599)BVBBV050171277 |
| edition | Pt. 1.2025- |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2025-02-18T09:00:45Z |
| institution | BVB |
| language | English |
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| series2 | Memoirs of the American Mathematical Society Series |
| spelling | Baker, Matthew 1973- Verfasser (DE-588)136700748 aut Foundations of Matroids Pt. 1.2025- Providence American Mathematical Society 2025- txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society Series ... Description based on publisher supplied metadata and other sources Cover -- Title page -- Introduction -- A quick introduction to pastures -- Representations of matroids over pastures and the foundation of a matroid -- Products and coproducts -- Universal cross ratios -- The structure theorem for foundations of matroids without large uniform minors -- Consequences of the structure theorem -- Content overview -- Acknowledgments -- Chapter 1. Background -- 1.1. Notation -- 1.2. The Tutte group -- 1.3. Embedded minors -- Chapter 2. Pastures -- 2.1. Definition and first properties -- 2.2. Matroid representations -- 2.3. Matroid representations via hyperplane functions -- 2.4. The universal pasture -- 2.5. The Tutte group and the universal pasture -- Chapter 3. Cross ratios -- 3.1. Cross ratios of -matroids -- 3.2. Cross ratios for hyperplanes -- 3.3. Universal cross ratios -- 3.4. Fundamental elements -- 3.5. Compatibility with the Tutte group formulation of Dress and Wenzel -- Chapter 4. Foundations -- 4.1. Definition and basic facts -- 4.2. Universal cross ratios as generators of the foundation -- 4.3. The foundation of the dual matroid -- 4.4. Foundations of embedded minors -- 4.5. The foundation of ²₄ -- 4.6. The tip and cotip relations -- 4.7. Relations for parallel elements -- 4.8. The foundation of the Fano matroid and its dual -- 4.9. A presentation of the foundation by hyperplanes -- 4.10. A presentation of the foundation by bases -- 4.11. A presentation of the foundation by embedded minors -- Chapter 5. The structure theorem -- 5.1. Foundations of matroids on 5 elements -- 5.2. Symmetry quotients -- 5.3. The structure theorem for matroids without large uniform minors -- Chapter 6. Applications -- 6.1. Forbidden minors for regular, binary and ternary matroids -- 6.2. Uniqueness of the rescaling class over F₃ -- 6.3. Criteria for representability over certain fields. Lorscheid, Oliver 1978- Verfasser (DE-588)1201611245 aut Erscheint auch als Online-Ausgabe, PDF |
| spellingShingle | Baker, Matthew 1973- Lorscheid, Oliver 1978- Foundations of Matroids |
| title | Foundations of Matroids |
| title_auth | Foundations of Matroids |
| title_exact_search | Foundations of Matroids |
| title_full | Foundations of Matroids |
| title_fullStr | Foundations of Matroids |
| title_full_unstemmed | Foundations of Matroids |
| title_short | Foundations of Matroids |
| title_sort | foundations of matroids |
| work_keys_str_mv | AT bakermatthew foundationsofmatroids AT lorscheidoliver foundationsofmatroids |