Relaxations of the matroid axioms I: Independence, Exchange and Circuits
Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial complexes. The resulting classes retain some of...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/6365/pdf |
| _version_ | 1827323950124761088 |
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| author | Jose ́ Alejandro Samper |
| author_facet | Jose ́ Alejandro Samper |
| author_sort | Jose ́ Alejandro Samper |
| collection | DOAJ |
| description | Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial complexes. The resulting classes retain some of the matroid properties and allow us to classify matroid properties according to the relevant axioms needed to prove them. We illustrate this by discussing Tutte polynomials. Furthermore, we extend a conjecture of Stanley on h-vectors and provide evidence to show that the extension is better suited than matroids to study the conjecture. |
| first_indexed | 2024-04-25T02:00:53Z |
| format | Article |
| id | doaj.art-a83b6caf02df4227bc5b48fc1c668136 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:53Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-a83b6caf02df4227bc5b48fc1c6681362024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.63656365Relaxations of the matroid axioms I: Independence, Exchange and CircuitsJose ́ Alejandro Samper0Department of Mathematics [Seattle]Motivated by a question of Duval and Reiner about higher Laplacians of simplicial complexes, we describe various relaxations of the defining axioms of matroid theory to obtain larger classes of simplicial complexes that contain pure shifted simplicial complexes. The resulting classes retain some of the matroid properties and allow us to classify matroid properties according to the relevant axioms needed to prove them. We illustrate this by discussing Tutte polynomials. Furthermore, we extend a conjecture of Stanley on h-vectors and provide evidence to show that the extension is better suited than matroids to study the conjecture.https://dmtcs.episciences.org/6365/pdfcombinatorics[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Jose ́ Alejandro Samper Relaxations of the matroid axioms I: Independence, Exchange and Circuits Discrete Mathematics & Theoretical Computer Science combinatorics [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | Relaxations of the matroid axioms I: Independence, Exchange and Circuits |
| title_full | Relaxations of the matroid axioms I: Independence, Exchange and Circuits |
| title_fullStr | Relaxations of the matroid axioms I: Independence, Exchange and Circuits |
| title_full_unstemmed | Relaxations of the matroid axioms I: Independence, Exchange and Circuits |
| title_short | Relaxations of the matroid axioms I: Independence, Exchange and Circuits |
| title_sort | relaxations of the matroid axioms i independence exchange and circuits |
| topic | combinatorics [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6365/pdf |
| work_keys_str_mv | AT josealejandrosamper relaxationsofthematroidaxiomsiindependenceexchangeandcircuits |