SERIE B INFORMATIK Universal Dimensional Visibility Representations for Graphs

Universal 3-Dimensional Visibility Representations for Graphs

This paper studies 3-dimensional visibility representations of graphs in which objects in 3-d correspond to vertices and vertical visibilities between these objects correspond to edges. We ask which classes of simple objects are universal, i.e. powerful enough to represent all graphs. In particular, we show that there is no constant k for which the class of all polygons having k or fewer sides ...

Recent Results on 3D Visibility Representation of Graphs

A visibility representation of a graph G maps vertices of G to sets in Euclidean space. An edge u; v occurs in G if and only if the objects representing u and v see each other according to some visibility rule. Stimulated by application-driven research on 2-dimensional visualization, interest has developed in nding good 3-dimensional visualizations of graphs. This paper reviews selected recent ...

Universal Central Extension of Current Superalgebras

Representation as well as central extension are two of the most important concepts in the theory of Lie (super)algebras. Apart from the interest of mathematicians, the attention of physicist are also drawn to these two subjects because of the significant amount of their applications in Physics. In fact for physicists, the study of projective representations of Lie (super)algebras  are very impo...

SERIE B - INFORMATIK Algorithmic Chernoff-Hoeffding Inequalities in Integer Programming

On generalized reduced representations of restricted Lie superalgebras in prime characteristic

Let $mathbb{F}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted Lie superalgebra over $mathbb{F}$. It is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. These quotient superalgebras are called the generalized reduced enveloping ...