Results 1  10
of
1,805
Generalized polygons in projective spaces
"... Generalized polygons are rank 2 geometries that were introduced by Jacques Tits in order to better understand the twisted triality groups, see [29]. As precursors of buildings, they were the spherical rank 2 buildings avantlalettre. The standard examples are related to simple algebraic groups of ..."
Abstract
 Add to MetaCart
Generalized polygons are rank 2 geometries that were introduced by Jacques Tits in order to better understand the twisted triality groups, see [29]. As precursors of buildings, they were the spherical rank 2 buildings avantlalettre. The standard examples are related to simple algebraic groups
Generalized Polygons and Extended Geometries
, 1992
"... Let $\triangle $ be an undirected graph. For each vertex $x $ of $\triangle $ , we will denote by $\triangle(x) $ the set of vertices adjacent to $x $. The girth of $\triangle $ is the minimal length of a circuit in $\Delta $ and the diameter the maximum distance between two vertices of $\triangle $ ..."
Abstract
 Add to MetaCart
$. A generahzed polygon is a bipartite graph with girth equal to twice the diameter. A generalized polygon of diameter $n $ is also called a generalized ngon or generalized triangle for $n=3 $ , quadrangle for $n=4$, etc. A generalized 2gon is just a complete bipartite graph. Suppose $\triangle
Generalized polygons, SCABS and GABS
 BUILDINGS AND THE GEOMETRY OF DIAGRAMS
, 1986
"... Recently there has been a great deal of activity in the geometric and group theoretic study of "buildinglike geometries" One of the directions of this activity has concerned GABs ("geometries that are almost buildings") and SCABs ("chamber systems that are almost buildings& ..."
Abstract

Cited by 7 (1 self)
 Add to MetaCart
Recently there has been a great deal of activity in the geometric and group theoretic study of "buildinglike geometries" One of the directions of this activity has concerned GABs ("geometries that are almost buildings") and SCABs ("chamber systems that are almost buildings"). (Other names for these are "chamber systems of type M" and "geometries of type M" in [Ti 7], and "Tits geometries of type M" or "Tits chamber systems of type M" in [AS; Tim 1,2]. ) The main goal of this paper is to survey these developments with special emphasis on their relationships with finite geometries.
Discrete Laplacians on General Polygonal Meshes
"... While the theory and applications of discrete Laplacians on triangulated surfaces are well developed, far less is known about the general polygonal case. We present here a principled approach for constructing geometric discrete Laplacians on surfaces with arbitrary polygonal faces, encompassing non ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
While the theory and applications of discrete Laplacians on triangulated surfaces are well developed, far less is known about the general polygonal case. We present here a principled approach for constructing geometric discrete Laplacians on surfaces with arbitrary polygonal faces, encompassing non
Compact generalized polygons and Moore graphs as stable graphs
, 2008
"... We introduce stable graphs as a common generalization of compact generalized polygons with closed adjacency, stable planes and other types of graphs with continuous geometric operations; nonbipartite structures like Moore graphs are also included. Topological and graphtheoretical properties of ..."
Abstract
 Add to MetaCart
We introduce stable graphs as a common generalization of compact generalized polygons with closed adjacency, stable planes and other types of graphs with continuous geometric operations; nonbipartite structures like Moore graphs are also included. Topological and graphtheoretical properties
Straight Skeletons for General Polygonal Figures in the Plane
, 1996
"... : A novel type of skeleton for general polygonal figures, the straight skeleton S(G) of a planar straight line graph G, is introduced and discussed. Exact bounds on the size of S(G) are derived. The straight line structure of S(G) and its lower combinatorial complexity may make S(G) preferable to th ..."
Abstract

Cited by 42 (2 self)
 Add to MetaCart
: A novel type of skeleton for general polygonal figures, the straight skeleton S(G) of a planar straight line graph G, is introduced and discussed. Exact bounds on the size of S(G) are derived. The straight line structure of S(G) and its lower combinatorial complexity may make S(G) preferable
Bounds for graphs of given girth and generalized polygons
, 2002
"... In this paper we present a bound for bipartite graphs with average bidegrees η and ξ satisfying the inequality η ≥ ξ α, α ≥ 1. This bound turns out to be the sharpest existing bound. Sizes of known families of finite generalized polygons are exactly on that bound. Finally, we present lower bounds f ..."
Abstract
 Add to MetaCart
In this paper we present a bound for bipartite graphs with average bidegrees η and ξ satisfying the inequality η ≥ ξ α, α ≥ 1. This bound turns out to be the sharpest existing bound. Sizes of known families of finite generalized polygons are exactly on that bound. Finally, we present lower bounds
Diamond, Hexagon, and General Polygonal Shaped Window Smoothing
"... Abstract. This paper presents fast recursive or moving windows algorithms for calculating local means in a diamond, hexagon and general polygonal shaped windows of an image. The algorithms for diamond shaped window require only seven or eight additions and subtractions per pixel. A number of other s ..."
Abstract
 Add to MetaCart
Abstract. This paper presents fast recursive or moving windows algorithms for calculating local means in a diamond, hexagon and general polygonal shaped windows of an image. The algorithms for diamond shaped window require only seven or eight additions and subtractions per pixel. A number of other
Results 1  10
of
1,805