The Space of Tropically Collinear Points Is Shellable

Tropical Linear Spaces and Tropical Convexity

In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult to see that each such space is tropically convex, i.e. closed under tropical linear combinations. However, we will also show that the conv...

Moving Three Collinear Griffith Cracks at Orthotropic Interface

This work deals with the interaction of P-waves between a moving central crack and a pair of outer cracks situated at the interface of an orthotropic layer and an elastic half-space. Initially, we considered a two-dimensional elastic wave equation in orthotropic medium. The Fourier transform has been applied to convert the basic problem to solve the set of four integral equations. These set of ...

THE SPACE OF n POINTS ON A TROPICAL LINE IN d-SPACE

The tropical semiring (R,min,+) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of n points on a tropical line in d-space, which is interpretable as the space of n-species phylogenetic trees. This is equivalent to the space of n × d matrices of tropical rank two, a simplici...

The Complement of a D-Tree is Pure Shellable

Bounds on $m_r(2,29)$

 An $(n, r)$-arc is a set of $n$ points of a projective plane such that some $r$, but no $r+1$ of them, are collinear. The maximum size of an $(n, r)$-arc in  PG(2, q) is denoted by $m_r(2,q)$. In this paper thirteen new $(n, r)$-arc in  PG(2,,29) and a table with the best known lower and upper bounds on $m_r(2,29)$ are presented. The results are obtained by non-exhaustive local computer search.