Cosmescu, Andrei Calin (2026) Finding interesting foundations using macaulay2. Bachelor's Thesis, Mathematics.
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Abstract
In this paper, we use the software macaulay2, more specifically the Matroids package developed by Justin Chen in order to compute foundations for matroids with 9 or more elements, specifically of rank 4 on 9 elements and of rank 3 on 10 and 11 elements, and we develop an algorithm to classify these foundations by finding their isomorphism classes. Finally, we use the database of foundations for specific applications such as looking for small foundations that don't correspond to already well-known pastures from literature as well as checking whether specific pastures count as matroid foundations. The database of foundations is made publicly available to enable further research in matroid representability. It can be accessed and used at https://doi.org/10.5281/zenodo.21292499.
| Item Type: | Thesis (Bachelor's Thesis) |
|---|---|
| Supervisor name: | Lorscheid, O. and Muller, J.S. |
| Degree programme: | Mathematics |
| Thesis type: | Bachelor's Thesis |
| Language: | English |
| Date Deposited: | 22 Jul 2026 08:41 |
| Last Modified: | 22 Jul 2026 08:41 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/37459 |
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