Combinatorial Types of Tropical Eigenvectors
  The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices. 
Bernd Sturmfels and Ngoc Mai Tran
math.CO cs.DM