Collineation Groups Whose Order is Prime to the Characteristic.
Collineations and Extensions of Translation Nets.
Collineations of Subiaco and Cherowitzo hyperovals.
Collineations of the Subiaco generalized quadrangles.
Colouring polytopic partitions in
We consider face-to-face partitions of bounded polytopes into convex polytopes in for arbitrary and examine their colourability. In particular, we prove that the chromatic number of any simplicial partition does not exceed . Partitions of polyhedra in into pentahedra and hexahedra are - and -colourable, respectively. We show that the above numbers are attainable, i.e., in general, they cannot be reduced.
Colouring polytopic partitions in
Combinatorial and group-theoretic compactifications of buildings
Let be a building of arbitrary type. A compactification of the set of spherical residues of is introduced. We prove that it coincides with the horofunction compactification of endowed with a natural combinatorial distance which we call the root-distance. Points of admit amenable stabilisers in and conversely, any amenable subgroup virtually fixes a point in . In addition, it is shown that, provided is transitive enough, this compactification also coincides with the group-theoretic...
Combinatorial Complexity Bounds for Arrangements of Curves and Spheres.
Combinatorial Geometries Representable over GF(3) and GF(q). I. The Number of Points.
Combinatorics, group theory and geometric models
Combinatorics of non-holonomous jets
Combing Euclidean buildings.
Compact 16-Dimensional Projective Planes with Large Collineation Groups.
Compact 16-dimensional Projective Planes with Large Collineation Groups. II.
Compact 16-dimensional Projective Planes with Large Collineation Groups. III.
Compact 8-dimensional Projective Planes.
Compact Disconnected Planes, Inverse Limits and Homomorphisms.
Compact groups of automorphisms of stable planes.
Compact hyperbolic Coxeter -polytopes with facets.
Compact hyperbolic tetrahedra with non-obtuse dihedral angles.
Given a combinatorial description C of a polyhedron having E edges, the space of dihedral angles of all compact hyperbolic polyhedra that realize C is generally not a convex subset of RE. If C has five or more faces, Andreev's Theorem states that the corresponding space of dihedral angles AC obtained by restricting to non-obtuse angles is a convex polytope. In this paper we explain why Andreev did not consider tetrahedra, the only polyhedra having fewer than five faces, by demonstrating that the...