Baumrekursionen und Rekursionen mit unregelmäßigem Abstieg

Non-regular recursions, which do not satisfy the schema of linear difference equations, define sequences with non-uniform growth. A good example is the heap sequence, which counts the number of heaps with n nodes. An important result is a new representation of the heap sequence. In order to analyse the growth, the sequence of quotients is considered. This sequence shows as asymptotic feature an oscillating behavior inside a convergence cone. The oscillation looks somewhat periodical and shows self-similarity phenomena. The analysis of cluster points, self-similarity etc. of the sequence of quotients is deeply connected with infinite labeled graphs, in particular binary trees. The structural properties of these graphs give answers to many problems which are involved here. An example of a property of the sequence of quotients, which is induced by subgraphs, is the set of cluster points. Uncountable sets of cluster points are connected with infinite paths in infinite binary trees. On the other hand infinite subtrees and similar substructures (not necessarily subgraphs) lead to the self-similarity of the sequence of quotients.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2002

Author dc:creator

• Bomble, Ferdinand Wolfgang

Contributors dc:contributor

• Oberschelp, Walter

• info:eu-repo/classification/ddc/004
• Informatik

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

ger

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-122050%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:60331