Matroids arising from algebraic shifting
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912745717235712 |
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| author | Guterman, Lazar Nevo, Eran |
| author_facet | Guterman, Lazar Nevo, Eran |
| contents | We characterize the shifted simple graphs and the $3$-uniform shifted hypergraphs whose inverse image under exterior shifting is the set of bases of a matroid: those are exactly the hypergraphs whose hyperedges form an initial lex-segment. There are several examples of known matroids arising in this way: the simplicial matroid, the hyperconnectivity matroid and the area-rigidity matroid. For $k\ge 4$, we provide a similar characterization for shifted $k$-uniform hypergraphs satisfying an additional combinatorial condition.
For symmetric shifting, we prove an analogous characterization for shifted simple graphs, where the classical generic rigidity matroid is an example of a matroid arising in this way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matroids arising from algebraic shifting Guterman, Lazar Nevo, Eran Combinatorics 05E45, 05B35, 13F55, 05C65 We characterize the shifted simple graphs and the $3$-uniform shifted hypergraphs whose inverse image under exterior shifting is the set of bases of a matroid: those are exactly the hypergraphs whose hyperedges form an initial lex-segment. There are several examples of known matroids arising in this way: the simplicial matroid, the hyperconnectivity matroid and the area-rigidity matroid. For $k\ge 4$, we provide a similar characterization for shifted $k$-uniform hypergraphs satisfying an additional combinatorial condition. For symmetric shifting, we prove an analogous characterization for shifted simple graphs, where the classical generic rigidity matroid is an example of a matroid arising in this way. |
| title | Matroids arising from algebraic shifting |
| topic | Combinatorics 05E45, 05B35, 13F55, 05C65 |
| url | https://arxiv.org/abs/2512.03294 |