کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10149840 1646775 2018 52 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Electroid varieties and a compactification of the space of electrical networks
ترجمه فارسی عنوان
انواع الکترودها و فشرده سازی فضای شبکه های الکتریکی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
چکیده انگلیسی
We construct a compactification of the space of circular planar electrical networks studied by Curtis-Ingerman-Morrow [4] and Colin de Verdière-Gitler-Vertigan [3], 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 uncrossing 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 338, 7 November 2018, Pages 549-600
نویسندگان
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