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Electroid varieties and a compactificati...

Lam, Thomas...

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Electroid varieties and a compactification of the space of electrical networks by Lam, Thomas ( Author )

Content Provider	Lemonjar Open Access
Publisher	Australian National University
Publication Date	01-09-2023
Summary	We construct a compactification of the space of circular planar electrical networks studied by Curtis-Ingerman-Morrow and De Verdiere-Gitler-Vertigan, using cactus networks. We embed this compactification as a linear slice of the totally nonnegative Grassmannian, and relate Kenyon and Wilson's grove measurements to Postnikov's boundary measurements. Intersections of the slice with the positroid stratification leads to a class of electroid varieties, indexed by matchings. The partial order on matchings arising from electrical networks is shown to be dual to a subposet of affine Bruhat order. The analogues of matroids in this setting are certain distinguished collections of non-crossing partitions.
ISBN	-
Item Type	Article
File Type	pdf
File Size	29.34 KB
Language	English
Subjects	-
Unlimited	MYR 0.01
Total read	-
URL	http://arxiv.org/abs/1402.6261

Citation

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AMA 11th EditionReferences

Lam, Thomas. Electroid varieties and a compactification of the space of electrical networks. Australian National University. September 01, 2023. Accessed September 20, 2024. https://online.provdatabase.com/cite/23168

APA 7th EditionReferences

Lam, Thomas. (2023). Electroid varieties and a compactification of the space of electrical networks. Australian National University. https://online.provdatabase.com/cite/23168

Chicago 17th EditionReferences

Lam, Thomas. Electroid varieties and a compactification of the space of electrical networks. Australian National University. 2023. https://online.provdatabase.com/cite/23168

HarvardReferences

Lam, Thomas. (2023). Electroid varieties and a compactification of the space of electrical networks. [Online]. Australian National University. Available from: https://online.provdatabase.com/cite/23168. (Accessed 20 September 2024).

Harvard AustraliaReferences

Lam, Thomas, 2023, Electroid varieties and a compactification of the space of electrical networks, Australian National University, viewed 20 September 2024, <https://online.provdatabase.com/cite/23168>

MLA 9th EditionWorks Cited

Lam, Thomas. Electroid varieties and a compactification of the space of electrical networks. Australian National University, 2023. PROV Database, https://online.provdatabase.com/cite/23168.

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