相关论文: Points and lines configurations for perpendicular …

When searching for small 4-configurations of points and lines, polycyclic configurations, in which every symmetry class of points and lines contains the same number of elements, have proved to be quite useful. In this paper we construct and…

Inspired by the Stochastic processes described by the Feller Coupling and Chinese Restaurant Processes, we create four different bijections from words in the set $[1]\times [2] \times\cdot \times[n]$ to $S_n$. We then compose these maps…

In this work we give precise asymptotic expressions on the probability of the existence of fixed-size components at the threshold of connectivity for random geometric graphs.

Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…

There has been considerable recent interest, primarily motivated by problems in applied algebraic topology, in the homology of random simplicial complexes. We consider the scenario in which the vertices of the simplices are the points of a…

The equitangent locus of a convex plane curve consists of the points from which the two tangent segments to the curve have equal length. The equitangent problem concerns the relation between the curve and its equitangent locus. An…

We determine the points of the epicyclic topos which plays a key role in the geometric encoding of cyclic homology and the lambda operations. We show that the category of points of the epicyclic topos is equivalent to projective geometry in…

This paper investigated the problem of embedding a simple Hamiltonian Cycle with n vertices on n points inside a simple polygon. This problem seeks to embed a straight-line cycle (without bends), which does not intersect either itself or…

In the projective plane over a finite field of characteristic not equal to 2, we compute the probability that a randomly selected pair of distinct conics $(\mathscr{A},\mathscr{B})$, with $\mathscr{A}$ smooth or singular and $\mathscr{B}$…

It has been known that the distribution of the random distances between two uniformly distributed points within a convex polygon can be obtained based on its chord length distribution (CLD). In this report, we first verify the existing…

Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…

Let six points $1, ...6$ lie in general position in the real projective plane and consider the pencil of nodal cubics based at these points, with node at one of them, say 1. This pencil has five reducible cubics. We call combinatorial cubic…

Given a set of points in the plane each colored either red or blue, we find non-self-intersecting geometric spanning cycles of the red points and of the blue points such that each edge of the red spanning cycle is crossed at most three…

We list all the possible fundamental groups of the complements of real conic-line arrangements with two conics which are tangent to each other at two points, with up to two additional lines. For the computations we use the topological local…

In this follow-up article to Symplectification of Circular Arcs and Arc Splines, biarc geometry is examined from a purely geometric point of view. Two given points together with their associated tangent vectors in the plane are sufficient…

A presymplectic structure on odd dimensional manifold is given by a closed 2-form which is nondegenerate, i.e., of maximal rank. We investigate geometry of presymplectic manifolds. Some basic theorems analogous to those in symplectic and…

We give a formula for the number of interior intersection points made by the diagonals of a regular $n$-gon. The answer is a polynomial on each residue class modulo 2520. We also compute the number of regions formed by the diagonals, by…

A new parametric surface representation is proposed that interpolates the vertices of a given closed mesh of arbitrary topology. Smoothly connecting quadrilateral patches are created by blending local, multi-sided quadratic interpolants. In…

In this article we combinatorially describe the triangles that are present in two types of line arrangements, those which have global cyclicity and those which are infinity type line arrangements. A combinatorial nomenclature has been…

We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. We give formulas for their dimension and vertex degree. In the…