Related papers: Lattice of Triangulations: the proof and an algori…
This article intends to characterize triangular norms on a finite lattice. We first give a method for generating a triangular norm on an atomistic lattice by the values of atoms. Then we prove that every triangular norm on a non-Boolean…
In the present paper we introduce a lattice-ordered partial monoid structure on a suitable set of multilayer networks. We first study a kind of mappings that preserve the partial order and describe the order structure. After that we define…
In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…
Flips of diagonals in colored triangle-free triangulations of a convex polygon are interpreted as moves between two adjacent chambers in a certain graphic hyperplane arrangement. Properties of geodesics in the associated flip graph are…
We associate to triangulations of infinite type surface a type of flip graph where simultaneous flips are allowed. Our main focus is on understanding exactly when two triangulations can be related by a sequence of flips. A consequence of…
We exhibit algorithms for calculating Tits' buildings and orbits of vectors in a lattice $L$ for certain subgroups of $\operatorname{O}(L)$. We discuss how these algorithms can be applied to understand the configuration of boundary…
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
Recently, cutting planes derived from maximal lattice-free convex sets have been studied intensively by the integer programming community. An important question in this research area has been to decide whether the closures associated with…
A simple-triangle graph is the intersection graph of triangles that are defined by a point on a horizontal line and an interval on another horizontal line. The time complexity of the recognition problem for simple-triangle graphs was a…
It has been proven that the lozenge tilings of a quartered hexagon on the triangular lattice are enumerated by a simple product formula. In this paper we give a new proof for the tiling formula by using Kuo's graphical condensation. Our…
A framework, which is a (possibly infinite) graph with a realization of its vertices in the plane, is called flexible if it can be continuously deformed while preserving the edge lengths. We focus on flexibility of frameworks in which…
A concept of a rectangular diagram of a foliation in the three-sphere is introduced. It is shown that any co-orientable finite depth foliation in the complement of a link admits a presentation by a rectangular diagram compatible with the…
The flip graph algorithm is a method for discovering new matrix multiplication schemes by following random walks on a graph. We introduce a version of the flip graph algorithm for matrix multiplication schemes that admit certain symmetries.…
By Dirichlet's Unit Theorem, under the log embedding the units in the ring of integers of a number field form a lattice, called the log-unit lattice. We investigate the geometry of these lattices when the number field is a biquadratic or…
We describe an efficient algorithm to compute a pseudotriangulation of a finite planar family of pairwise disjoint convex bodies presented by its chirotope. The design of the algorithm relies on a deepening of the theory of visibility…
A tanglegram consists of two rooted binary trees and a perfect matching between their leaves, and a planar tanglegram is one that admits a layout with no crossings. We show that the problem of generating planar tanglegrams uniformly at…
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and for the regularization of such a graph by the minimization…
The goal of this paper is to design a simplex algorithm for linear programs on lattice polytopes that traces `short' simplex paths from any given vertex to an optimal one. We consider a lattice polytope $P$ contained in $[0,k]^n$ and…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
We describe a simple algorithm for classifying orbits into orbit families. This algorithm works by finding patterns in the sign changes of the principal coordinates. Orbits in the logarithmic potential are studied as an application; we…