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| Format: | Preprint |
| Published: |
2020
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| Online Access: | https://arxiv.org/abs/2001.05535 |
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| _version_ | 1866910461156392960 |
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| author | Grinberg, Darij |
| author_facet | Grinberg, Darij |
| contents | Inspired by Manjul Bhargava's theory of generalized factorials, Fedor Petrov and the author have defined the "Bhargava greedoid" -- a greedoid (a matroid-like set system on a finite set) assigned to any "ultra triple" (a somewhat extended variant of a finite ultrametric space). Here we show that the Bhargava greedoid of a finite ultra triple is always a "Gaussian elimination greedoid" over any sufficiently large (e.g., infinite) field; this is a greedoid analogue of a representable matroid. We find necessary and sufficient conditions on the size of the field to ensure this. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_05535 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | The Bhargava greedoid as a Gaussian elimination greedoid Grinberg, Darij Combinatorics Discrete Mathematics 05B35, 12J25 Inspired by Manjul Bhargava's theory of generalized factorials, Fedor Petrov and the author have defined the "Bhargava greedoid" -- a greedoid (a matroid-like set system on a finite set) assigned to any "ultra triple" (a somewhat extended variant of a finite ultrametric space). Here we show that the Bhargava greedoid of a finite ultra triple is always a "Gaussian elimination greedoid" over any sufficiently large (e.g., infinite) field; this is a greedoid analogue of a representable matroid. We find necessary and sufficient conditions on the size of the field to ensure this. |
| title | The Bhargava greedoid as a Gaussian elimination greedoid |
| topic | Combinatorics Discrete Mathematics 05B35, 12J25 |
| url | https://arxiv.org/abs/2001.05535 |