{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:60331"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:60331","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Baumrekursionen und Rekursionen mit unregelmäßigem Abstieg","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Bomble, Ferdinand Wolfgang"],"institution":"Publikationsserver der RWTH Aachen University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Oberschelp, Walter"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2002,"date_issued":"2002","date_published":"2002","updated_at":"2026-07-30T19:42:56Z","subjects":["info:eu-repo/classification/ddc/004","Informatik"],"languages":["ger"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-122050%22"],"render_values":[{"text":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-122050%22","href":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-122050%22","code":true}]}]},"links":{"outbound_url":"https://publications.rwth-aachen.de/record/60331","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Oberschelp, Walter"]},{"key":"dc:creator","label":"Author","values":["Bomble, Ferdinand Wolfgang"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:coverage","label":"Dc Coverage","values":["DE"]},{"key":"dc:date","label":"Dc Date","values":["2002"]},{"key":"dc:publisher","label":"Institution","values":["Publikationsserver der RWTH Aachen University"]},{"key":"dc:relation","label":"Dc Relation","values":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-3867"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["info:eu-repo/classification/ddc/004","Informatik"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["ger"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/record/60331","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-122050%22"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Publikationsserver der RWTH Aachen University XVI, 259 S. : graph. Darst. (2002). = Aachen, Techn. Hochsch., Diss., 2002"]},{"key":"dc:title","label":"Title","values":["Baumrekursionen und Rekursionen mit unregelmäßigem Abstieg"]}]}],"canonical_facts":{"dc:contributor":["Oberschelp, Walter"],"dc:coverage":["DE"],"dc:creator":["Bomble, Ferdinand Wolfgang"],"dc:date":["2002"],"dc:description":["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."],"dc:identifier":["https://publications.rwth-aachen.de/record/60331","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-122050%22"],"dc:language":["ger"],"dc:publisher":["Publikationsserver der RWTH Aachen University"],"dc:relation":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-3867"],"dc:rights":["info:eu-repo/semantics/openAccess"],"dc:source":["Aachen : Publikationsserver der RWTH Aachen University XVI, 259 S. : graph. Darst. (2002). = Aachen, Techn. Hochsch., Diss., 2002"],"dc:subject":["info:eu-repo/classification/ddc/004","Informatik"],"dc:title":["Baumrekursionen und Rekursionen mit unregelmäßigem Abstieg"],"dc:type":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]},"updated_at":"2026-07-30T19:42:56Z"}