by Johannes Böhm
Preprint series: 09-04 , Reports on Algebra and Geometry
Abstract: In spaces of constant curvature (= ±1; elliptic, hyperbolic or generalized hyperbolic) the types of orthoschemes and the types of the Napier cycles are of interest. The aim is to calculate the numbers of these types for each dimension. This is possible with the help of a special theory for permutations, called geometric permutations and periodic permutations. In Part III the several types of the Napier cycles and therefore also of the hyperbolic kernels are discussed. The possibility of counting recursively their numbers for each dimension is explained. For the formulated Lemmata the proofs are given in this appendix. For several special cases these numbers are explicitly given.
Keywords: Hyperbolic and elliptic geometries and generalizations, n-dimensional polytopes, orthoschems, permutations, Napier cycles, hyperbolic kernels