Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral
tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the …

Tropical mathematics has found many applications in both pure and applied areas, as
documented by a growing number of monographs on its interactions with various other …

The spinor variety is cut out by the quadratic Wick relations among the principal Pfaffians of
an n× n skew-symmetric matrix. Its points correspond to n-dimensional isotropic subspaces …

The-associahedron is the simplicial complex of-crossing-free subgraphs of the complete
graph with vertices on a circle. Its facets are called-triangulations. We explore the connection …

We initiate the study of positive-tropical generators as positive analogues of the concept of
tropical bases. Applying this to the tropicalization of determinantal varieties, we develop …

We initiate the study of positive-tropical generators as positive analogues of the concept of
tropical bases. Applying this to the tropicalization of determinantal varieties, we develop …

In just ten years, tropical geometry has established itself as an important new field bridging
algebraic geometry and combinatorics whose techniques have been used to attack …

The computation of the tropical prevariety is the first step in the application of polyhedral
methods to compute positive dimensional solution sets of polynomial systems. In particular …

We show that the r-by-r minors of a d-by-n matrix of variables form a tropical basis of the
ideal they generate if and only if one of the following conditions holds:(i) r⩽ 3,(ii) r= min {d …

arXiv:1012.5507v1 [math.CO] 26 Dec 2010 Page 1 arXiv:1012.5507v1 [math.CO] 26 Dec 2010
EXAMPLE OF A 6-BY-6 MATRIX WITH DIFFERENT TROPICAL AND KAPRANOV RANKS …