Related papers: Finding or counting all shellings of a simplicial …
We study a class of mechanisms known as Kokotsakis polyhedra with a quadrangular base. These are $3\times3$ quadrilateral meshes whose faces are rigid bodies and joined by hinges at the common edges. In contrast to existing work, the…
We study partitions of totally positive integers in real quadratic fields. We develop an algorithm for computing the number of partitions, prove a result about the parity of the partition function, and characterize the quadratic fields such…
Consider a graph with a rotation system, namely, for every vertex, a circular ordering of the incident edges. Given such a graph, an angle cover maps every vertex to a pair of consecutive edges in the ordering -- an angle -- such that each…
The usual methods for root finding of polynomials are based on the iteration of a numerical formula for improvement of successive estimations. The unpredictable nature of the iterations prevents to search roots inside a pre-specified region…
An algorithm is presented that constructs an acyclic partial matching on the cells of a given simplicial complex from a vector-valued function defined on the vertices and extended to each simplex by taking the least common upper bound of…
How complex must two finite 2-complexes be to admit a common, but not finite common, covering? We obtain an almost answer: the minimum possible number of triangles in a pseudo-simplicial triangulation of each complex is 3, 4, or 5.
A fully implementable filtered polynomial approximation on spherical shells is considered. The method proposed is a quadrature-based version of a filtered polynomial approximation. The radial direction and the angular direction of the…
A facet of an hyperplane arrangement is called external if it belongs to exactly one bounded cell. The set of all external facets forms the envelope of the arrangement. The number of external facets of a simple arrangement defined by $n$…
Detecting and recognizing faces accurately has always been a challenge. Differentiating facial features, training images, and producing quick results require a lot of computation. The REaL system we have proposed in this paper discusses its…
This research starts with the observation that face recognition can suffer a low impact from significant image shrinkage. To explain this fact, we proposed the Pixel Clustering methodology. It defines regions in the image in which its…
There are a large number of theorems detailing the homological properties of the Stanley--Reisner ring of a simplicial complex. Here we attempt to generalize some of these results to the case of a simplicial poset. By investigating the…
The complete sets of irreducible triangulations are known for the orientable surfaces with genus of 0, 1, or 2 and for the nonorientable surfaces with genus of 1, 2, 3, or 4. By examining these sets we determine some of the properties of…
We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the $s$-uniform variant of the problem is…
In this paper, we present an effective method to characterize completely when a disconnected fractal square has only finitely many connected components. Our method is to establish some graph structures on fractal squares to reveal the…
In this paper we introduce two new methods for constructing injective resolutions of sheaves of finite-dimensional vector spaces on finite posets. Our main result is the existence and uniqueness of a minimal injective resolution of a given…
Ehrenborg, Govindaiah, Park, and Readdy recently introduced the van der Waerden complex, a pure simplicial complex whose facets correspond to arithmetic progressions. Using techniques from combinatorial commutative algebra, we classify when…
We develop a recursive formula for counting the number of rectangulations of a square, i.e the number of combinatorially distinct tilings of a square by rectangles. Our formula specializes to give a formula counting generic rectangulations,…
We present an approach to characterize genuine multiparticle entanglement using appropriate approximations in the space of quantum states. This leads to a criterion for entanglement which can easily be calculated using semidefinite…
By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be…
The article discusses a method for automating the process of cutting a honeycomb block, and specifically obtaining points and cutting angles for the required faces. The following requirements are taken into account in the calculations: the…