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Tropical planar networks

Stéphane Gaubert 1, 2 Adi Niv 3
1 TROPICAL - TROPICAL
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France
Abstract : We show that every tropical totally positive matrix can be uniquely represented as the transfer matrix of a canonical totally connected weighted planar network. We deduce a uniqueness theorem for the factorization of a tropical totally positive in terms of elementary Jacobi matrices.
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https://hal.inria.fr/hal-02423904
Contributor : Stephane Gaubert <>
Submitted on : Thursday, December 26, 2019 - 11:37:16 AM
Last modification on : Monday, March 29, 2021 - 2:47:34 PM

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  • HAL Id : hal-02423904, version 1
  • ARXIV : 1910.12934

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Stéphane Gaubert, Adi Niv. Tropical planar networks. Linear Algebra and its Applications, Elsevier, 2020, 595, pp.123-144. ⟨hal-02423904⟩

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