Tropical planar networks

Author : Adi Niv, Stephane Gaubert

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 : Planar networks, total positivity, total nonnegativity, compound matrix, permanent.

Conference Name : International Conference on Discrete Mathematics and Combinatorial Applications (ICDMCA-26)

Conference Place : Paris, France

Conference Date : 23rd Sep 2026