Radical relations in unitary, symplectic, and orthogonal groups.
Ramsey partitions and proximity data structures
This paper addresses two problems lying at the intersection of geometric analysis and theoretical computer science: The non-linear isomorphic Dvoretzky theorem and the design of good approximate distance oracles for large distortion.We introduce the notion of Ramsey partitions of a finite metric space, and show that the existence of good Ramsey partitions implies a solution to the metric Ramsey problem for large distortion (also known as the non-linear version of the isomorphic Dvoretzky theorem,...
Reflection loops of spaces with congruence and hyperbolic incidence structure
In an absolute space with congruence there are line reflections and point reflections. With the help of point reflections one can define in a natural way an addition + of points which is only associative if the product of three point reflection is a point reflection again. In general, for example for the case that is a linear space with hyperbolic incidence structure, the addition is not associative. is a K-loop or a Bruck loop.
Relationen zwischen Symmetrien in orthogonalen Gruppen.
Relationen zwischen symplektischen Transvektionen.
Remark on "Planes with analogues to Eucledian angular bisectors".
Réseaux de Coxeter-Davis et commensurateurs
For each integer and each finite graph , we construct a Coxeter group and a non positively curved polygonal complex on which acts properly cocompactly, such that each polygon of has edges, and the link of each vertex of is isomorphic to . If is a “generalized -gon”, then is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on for to be non enumerable (which is satisfied if is a thick classical generalized -gon). On the other hand,...
Root systems for two dimensional complex reflection groups.
Rotation du sous-espace invariant d’un endomorphisme symétrique de par une perturbation symétrique