Related papers: Counting Triangulations of Configurations
We report on enumerating the triangulations of cyclic polytopes with the new software mptopcom. This is relevant for its connection with higher Stasheff-Tamari orders, which occur in category theory and algebraic combinatorics.
We consider the combinatorial question of how many convex polygons can be made by using the edges taken from a fixed triangulation of n vertices. For general triangulations, there can be exponentially many: we show a construction that has…
We study the problem of finding maximum-area triangles that can be inscribed in a polygon in the plane. We consider eight versions of the problem: we use either convex polygons or simple polygons as the container; we require the triangles…
We describe the statistics of checkerboard triangulations obtained by colouring black every other triangle in triangulations of convex polygons.
We propose new algorithms for computing triangular decompositions of polynomial systems incrementally. With respect to previous works, our improvements are based on a {\em weakened} notion of a polynomial GCD modulo a regular chain, which…
We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
We characterize the topological configurations of points and lines that may arise when placing n points on a circle and drawing the n perpendicular bisectors of the sides of the corresponding convex cyclic n-gon. We also provide exact and…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
A {\em $1-$vertex triangulation} of an oriented compact surface $S$ of genus $g$ is an embedded graph $T\subset S$ with a unique vertex such that all connected components of $S\setminus T$ are triangles (adjacent to exactly 3 edges of $T$).…
We present a triangulation--independent area--ordering prescription which naturally generalizes the well known path ordering one. For such a prescription it is natural that the two--form ``connection'' should carry three ``color'' indices…
We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration…
The central component of a polygon triangulation is defined as the triangle or diameter that contain its geometric center. More generally, every polygon dissection contains a central component. Using this notion, we derive new recurrences…
We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…
A polynomial triangle is an array whose inputs are the coefficients in integral powers of a polynomial. Although polynomial coefficients have appeared in several works, there is no systematic treatise on this topic. In this paper we plan to…
We suggest an axiom system for a collection of matchings that describes the triangulation of product of simplices.
In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.
A typical census of 3-manifolds contains all manifolds (under various constraints) that can be triangulated with at most n tetrahedra. Al- though censuses are useful resources for mathematicians, constructing them is difficult: the best…
We define the notion of an approximate triangulation for a manifold $M$ embedded in euclidean space. The basic idea is to build a nested family of simplicial complexes whose vertices lie in $M$ and use persistent homology to find a complex…
This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex…