Generalized hyperbolic Napier cycles and their hyperbolic kernels 3

by    Johannes Böhm

Preprint series: 09-04 , Reports on Algebra and Geometry

51M10 Hyperbolic and elliptic geometries (general) and generalizations
51M20 Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]
52B11 $n$-dimensional polytopes
05A05 Combinatorial choice problems (subsets, representatives, permutations)
11B75 Other combinatorial number theory

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

Upload: 2009-07-14

The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.