Geodesic
Electrical networks and the grove algebra
Canadian journal of mathematics, Tome 77 (2025) no. 2, pp. 631-664

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DOI

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 analog 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.
DOI : 10.4153/S0008414X24000105
Mots-clés : Electrical network, grove, Gröbner basis, medial graph, Catalan object 
Gao, Yibo; Lam, Thomas; Xu, Zixuan. Electrical networks and the grove algebra. Canadian journal of mathematics, Tome 77 (2025) no. 2, pp. 631-664. doi: 10.4153/S0008414X24000105
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