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The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra
generalized triangle inequalities symmetric spaces and buildings applications to algebra
2015/10/14
In this paper we apply our results on the geometry of polygons in infinitesimal symmetric spaces, symmetric spaces and buildings, [KLM1, KLM2], to four problems in algebraic group theory. Two of these...
Most quasi-Monte Carlo research focuses on sampling from the unit
cube. Many problems, especially in computer graphics, are de ned via
quadrature over the unit triangle. Quasi-Monte Carlo methods fo...
Abstract: We show that the triangle with angles Pi/12, Pi/3 and 7*Pi/12 has the lattice property and compute this triangle's Veech group.
Scott's induced subdivision conjecture for maximal triangle-free graphs
Scott's subdivision conjecture maximal triangle-free graphs Combinatorics
2011/9/14
Abstract: Scott conjectured that the class of graphs with no induced subdivision of a given graph is $\chi$-bounded. We verify his conjecture for maximal triangle-free graphs.
Eigenstructure of the discrete Laplacian on the equilateral triangle: The Dirichlet & Neumann problems
equilateral triangle discrete Laplacian eigenvalues/eigenvectors
2010/11/1
Lam´e’s formulas for the eigenvalues and eigenfunctions of the continuous Laplacian on an equilateral triangle under Dirichlet and Neumann boundary conditions are herein extended to the discrete...
The incenter of a triangle as a cone isoperimetric center
Incenter isoperimetric problem optimization center
2011/3/1
We show that the the image of the regular projection of a vertex of a cone over a triangle
that minimizes the ratio of the cube of the area of the boundary of the cone and the square
of the volume o...
If G is a group with a presentation of the form hx, y|x3 = y3 = W(x, y)2 = 1i, then either G
is virtually soluble or G contains a free subgroup of rank 2. This provides additional evidence
in favour...
The Fractional Chromatic Number of Triangle-free Graphs with $\Delta\leq 3$
Triangle-free Graphs Combinatorics
2010/11/18
Let $G$ be any triangle-free graph with maximum degree $\Delta\leq 3$. Staton proved that the independence number of $G$ is at least $\frac{5}{14}n$. Heckman and Thomas conjectured that Staton's resul...
A probabilistic comparison of the strength of split, triangle, and quadrilateral cuts (extended version)
probabilistic comparison strength of split, triangle quadrilateral cuts
2010/12/13
We consider mixed integer linear programs defined by two equations involving two integer variables and non-negative continuous variables. The non-trivial facet-defining inequalities of such problems c...
Generalized triangle inequalities in thick Euclidean buildings of rank 2
Generalized triangle inequalities thick Euclidean buildings of rank 2
2010/12/1
We give the generalized triangle inequalities which determine the possible -valued side lengths of n-gons in thick Euclidean buildings of rank 2.
Dense graphs with a large triangle cover have a large triangle packing
Dense graphs with large triangle cover large triangle packing
2010/11/29
It is well known that a graph with m edges can be made triangle-free by removing (slightly less
than) m/2 edges. On the other hand, there are many classes of graphs which are hard to make
triangle-f...
Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux
Triangle-Free Triangulations Hyperplane Arrangements Shifted Tableaux
2010/12/6
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 geodesi...
Multiplying Pessimistic Estimators:Deterministic Approximation of Max TSP and Maximum Triangle Packing
derandomization approximation algorithms pessimistic estimators maximum traveling salesman problem
2012/12/3
We give a generalization of the method of pessimistic estimators, in which we compose estimators by multiplying them. We give conditions on the pessimistic estimators of two expectations, under which ...
Edge Coloring of Triangle-Free 1-Planar Graphs.
The Best Constants for a Double Inequality in a Triangle
Inequality Best Constant Triangle
2010/1/22
In this short note, by using some of Chen's theorems and classic analysis, we obtain a double inequality for triangle and give a positive answer to a problem posed by Yang and Yin [6].