2012/05/14 by Ngoc Mai Tran, Tran, Ngoc M.
Computer Science · Mathematics · #52B05 #52B20 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1205.3186
openalex publication_date 2012/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The map which takes a square matrix A to its polytrope is piecewise linear. We show that cones of linearity of this map form a polytopal fan partition of \Rn × n, whose face lattice is anti-isomorphic to the lattice of complete set of connected relations. This fan refines the non-fan partition of \Rn × n corresponding to cones of linearity of the eigenvector map. Our results answer open questions in a previous work with Sturmfels and lead to a new combinatorial classification of polytropes and tropical eigenspaces.