A categorification for the characteristic polynomial of matroids
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929485525286912 |
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| author | Saito, Takuya Yamagata, So |
| author_facet | Saito, Takuya Yamagata, So |
| contents | In the present paper, we provide a cohomology group as a categorification of the characteristic polynomial of matroids. The construction depends on the ``quasi-representation'' of a matroid. For a certain choice of the quasi-representation, we show that our cohomology theory gives a generalization of the chromatic cohomology introduced by L. Helme-Guizon and Y. Rong, and also the characteristic cohomology introduced by Z. Dancso and A. Licata. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09851 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A categorification for the characteristic polynomial of matroids Saito, Takuya Yamagata, So Combinatorics Algebraic Topology Geometric Topology 05B35, 05C15, 05C31, 57K18 In the present paper, we provide a cohomology group as a categorification of the characteristic polynomial of matroids. The construction depends on the ``quasi-representation'' of a matroid. For a certain choice of the quasi-representation, we show that our cohomology theory gives a generalization of the chromatic cohomology introduced by L. Helme-Guizon and Y. Rong, and also the characteristic cohomology introduced by Z. Dancso and A. Licata. |
| title | A categorification for the characteristic polynomial of matroids |
| topic | Combinatorics Algebraic Topology Geometric Topology 05B35, 05C15, 05C31, 57K18 |
| url | https://arxiv.org/abs/2402.09851 |