Electrical networks and the Grove algebra
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913742974877696 |
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| author | Gao, Yibo Lam, Thomas Xu, Zixuan |
| author_facet | Gao, Yibo Lam, Thomas Xu, Zixuan |
| contents | We study the ring of regular functions on the space of planar electrical networks, which we coin the grove algebra. This algebra is an electrical analogue of the Plücker ring studied classically in invariant theory. We develop the combinatorics of double groves to study the grove algebra, and find a quadratic Gröbner basis for the grove ideal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_12798 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Electrical networks and the Grove algebra Gao, Yibo Lam, Thomas Xu, Zixuan Combinatorics Commutative Algebra Algebraic Geometry We study the ring of regular functions on the space of planar electrical networks, which we coin the grove algebra. This algebra is an electrical analogue of the Plücker ring studied classically in invariant theory. We develop the combinatorics of double groves to study the grove algebra, and find a quadratic Gröbner basis for the grove ideal. |
| title | Electrical networks and the Grove algebra |
| topic | Combinatorics Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2208.12798 |