Tropical planar networks
Commutative Algebra
2019-10-30 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1910.12934,
title = {Tropical planar networks},
author = {Stephane Gaubert and Adi Niv},
journal= {arXiv preprint arXiv:1910.12934},
year = {2019}
}
Comments
The first author acknowledges the support of the Gaspard Monge (PGMO) program of Fondation Mathematique Hadamard, EDF, Orange and Thales, of the ICODE institute of Paris-Saclay, also of Labex Hadamard. This work started when the second author was with INRIA, being supported by the Chateaubriand program from the French Ministery of Foreign Affairs and by an INRIA fellowship