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 …

Triangulations presents the first comprehensive treatment of the theory of secondary
polytopes and related topics. The text discusses the geometric structure behind the …

The goal of this book is to explain, at the graduate student level, connections between
tropical geometry and optimization. Building bridges between these two subject areas is …

We present results on the number of linear regions of the functions that can be represented
by artificial feedforward neural networks with maxout units. A rank-maxout unit is a function …

The Dressian and the tropical Grassmannian parameterize abstract and realizable tropical
linear spaces; but in general, the Dressian is much larger than the tropical Grassmannian …

We are interested in the set of all subdivisions or triangulations of a given polytope P and
with a fixed finite set V of points that can be used as vertices. V must contain the vertices of …

The tropical Stiefel map associates to a tropical matrix A its tropical Plücker vector of
maximal minors, and thus a tropical linear space L (A). We call the L (A) s obtained in this …

We introduce a class of combinatorial singularities of Lagrangian skeleta of symplectic
manifolds. The link of each singularity is a finite regular cell complex homotopy equivalent to …

In this paper, we exploit the combinatorics and geometry of triangulations of products of
simplices to derive new results in the context of Catalan combinatorics of $\nu $-Tamari …

Enumerative combinatorics is about counting. The typical question is to find the number of
objects with a given set of properties. However, enumerative combinatorics is not just about …