相关论文: On the Pappus arrangement of lines, forth and back…
This paper continues the investigation of the configuration space of two distinct points on a graph. We analyze the process of adding an additional edge to the graph and the resulting changes in the topology of the configuration space. We…
Patterns of avoidance, adjacency, and association in complex systems design emerge from the system's underlying logical architecture (functional relationships among components) and physical architecture (component physical properties and…
We study tilings of the plane composed of two repeating tiles of different assigned areas relative to an arbitrary periodic lattice. We classify isoperimetric configurations (i.e., configurations with minimal length of the interfaces) both…
Given a line arrangement $\cal A$ with $n$ lines, we show that there exists a path of length $n^2/3 - O(n)$ in the dual graph of $\cal A$ formed by its faces. This bound is tight up to lower order terms. For the bicolored version, we…
The aim of this paper, triggered by some discussions in the astrophysics community raised by astro-ph/0508529, is to introduce the issue of `fits' from a probabilistic perspective (also known as Bayesian), with special attention to the…
In these notes we study hyperplane arrangements having at least one logarithmic derivation of degree two that is not a combination of degree one logarithmic derivations. It is well-known that if a hyperplane arrangement has a linear…
This short note has a twofold purpose: (i) to solve the question that motivates a recent paper of D. Popa on multilinear variants of Pietsch's composition theorem for absolutely summing operators. More precisely, we remark that there is a…
In a series of four papers we determine structures whose existence is dual, in the sense of complementary, to the existence of stars or combs. In the first paper of our series we determined structures that are complementary to arbitrary…
In this paper we obtain presentations of fundamental groups of the complements of three quadric-line arrangements in P^2. The first arrangement is a smooth quadric Q with n tangent lines to Q, and the second one is a quadric Q with n lines…
In my 1993 paper, "Pappus's Theorem and the Modular Group", I explained how the iteration of Pappus's Theorem gives rise to a $2$-parameter family of representations of the modular group into the group of projective automorphisms. In this…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
We introduce an algorithm that exploits a combinatorial symmetry of an arrangement in order to produce a geometric reflection between two disconnected components of its moduli space. We apply this method to disqualify three real examples…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
We prove configuration theorems that generalize the Desargues, Pascal, and Pappus theorems. Our generalization of the Desargues theorem allows us to introduce the structure of an Abelian group on the (properly extended) set of triangles…
The concept of configuration was first introduced to give a characterization for the amenability of groups. Then the concept of two-sided configuration was suggested to provide normality to study the group structures more efficiently. It…
The SHGH conjecture proposes a solution to the question of how many conditions a general union of fat points imposes on the complete linear system of curves in $\mathbb P^2$ of fixed degree $d$, and it is known to be true in many cases. We…
The two basic equations satisfied by the parameters of a block design define a three-dimensional affine variety $\mathcal{D}$ in $\mathbb{R}^{5}$. A point of $\mathcal{D}$ that is not in some sense trivial lies on four lines lying in…
In the present note we study combinatorial and algebraic properties of cubic-line arrangements in the complex projective plane admitting nodes, ordinary triple and $A_{5}$ singular points. We deliver a Hirzebruch-type inequality for such…
We consider the structure of the plane-line incidence matrix of the projective space $\mathrm{PG}(3,q)$ with respect to the orbits of planes and lines under the stabilizer group of the twisted cubic. Structures of submatrices with…