Electrical networks and the Grove algebra
arXiv:2208.12798 · doi:10.4153/S0008414X24000105
Abstract
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.
arXiv comment32 pages, 10 figures
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