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Mathematics > Combinatorics

arXiv:1809.10100 (math)
[Submitted on 26 Sep 2018 (v1), last revised 1 Jun 2022 (this version, v5)]

Title:Matroids arising from electrical networks

Authors:Bob Lutz
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Abstract:This paper introduces Dirichlet matroids, a generalization of graphic matroids arising from electrical networks. We present four main theorems. First, we exhibit a matroid quotient involving geometric duals of networks embedded in surfaces with boundary. Second, we characterize the Bergman fans of Dirichlet matroids as subfans of graphic Bergman fans. Third, we prove an interlacing result on the real zeros and poles of the trace of the response matrix. And fourth, we bound the coefficients of the precoloring polynomial of a network by the coefficients of the associated chromatic polynomial.
Comments: 26 pages, 12 figures
Subjects: Combinatorics (math.CO)
MSC classes: 05B35, 05C22 (Primary) 05C15, 05C40, 34B45 (Secondary)
Cite as: arXiv:1809.10100 [math.CO]
  (or arXiv:1809.10100v5 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1809.10100
Journal reference: Adv. Appl. Math., vol. 137 (2022)
Related DOI: https://doi.org/10.1016/j.aam.2022.102331

Submission history

From: Bob Lutz [view email]
[v1] Wed, 26 Sep 2018 16:16:32 UTC (260 KB)
[v2] Fri, 28 Sep 2018 07:36:07 UTC (260 KB)
[v3] Wed, 25 Sep 2019 22:01:00 UTC (701 KB)
[v4] Thu, 24 Oct 2019 01:06:22 UTC (714 KB)
[v5] Wed, 1 Jun 2022 02:56:57 UTC (302 KB)
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