{"id":"https://openalex.org/W2112514007","doi":"https://doi.org/10.1017/s0963548304006728","title":"Paradoxical Decompositions and Growth Conditions","display_name":"Paradoxical Decompositions and Growth Conditions","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2112514007","doi":"https://doi.org/10.1017/s0963548304006728","mag":"2112514007"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548304006728","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548304006728","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000595324","display_name":"G\u00e1bor Elek","orcid":"https://orcid.org/0000-0002-5105-7184"},"institutions":[{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"G\u00c1BOR ELEK","raw_affiliation_strings":["Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary (e-mail:","Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary (e-mail: [email\u00a0protected], [email\u00a0protected])#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary (e-mail:","institution_ids":["https://openalex.org/I7597260"]},{"raw_affiliation_string":"Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary (e-mail: [email\u00a0protected], [email\u00a0protected])#TAB#","institution_ids":["https://openalex.org/I7597260"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029190676","display_name":"Vera T. S\u00f3s","orcid":null},"institutions":[{"id":"https://openalex.org/I7597260","display_name":"Hungarian Academy of Sciences","ror":"https://ror.org/02ks8qq67","country_code":"HU","type":"government","lineage":["https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"VERA T. S\u00d3S","raw_affiliation_strings":["Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary (e-mail:","Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary (e-mail: [email\u00a0protected], [email\u00a0protected])#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary (e-mail:","institution_ids":["https://openalex.org/I7597260"]},{"raw_affiliation_string":"Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary (e-mail: [email\u00a0protected], [email\u00a0protected])#TAB#","institution_ids":["https://openalex.org/I7597260"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I7597260"],"apc_list":null,"apc_paid":null,"fwci":0.4153,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.62927315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"14","issue":"1-2","first_page":"81","last_page":"105"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.9882000088691711,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13297","display_name":"History and advancements in chemistry","score":0.9814000129699707,"subfield":{"id":"https://openalex.org/subfields/1606","display_name":"Physical and Theoretical Chemistry"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/art-history","display_name":"Art history","score":0.4053875803947449},{"id":"https://openalex.org/keywords/history","display_name":"History","score":0.2831689119338989}],"concepts":[{"id":"https://openalex.org/C52119013","wikidata":"https://www.wikidata.org/wiki/Q50637","display_name":"Art history","level":1,"score":0.4053875803947449},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.2831689119338989}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548304006728","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548304006728","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:real.mtak.hu:110692","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400081","display_name":"Repository of the Academy's Library (Library of the Hungarian Academy of Sciences)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210140733","host_organization_name":"Library and Information Centre of the Hungarian Academy of Sciences","host_organization_lineage":["https://openalex.org/I4210140733"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W30377398","https://openalex.org/W174051901","https://openalex.org/W207226365","https://openalex.org/W763244836","https://openalex.org/W787613230","https://openalex.org/W851845004","https://openalex.org/W1014277405","https://openalex.org/W1497035321","https://openalex.org/W1520357511","https://openalex.org/W1528152028","https://openalex.org/W1532790179","https://openalex.org/W1533602140","https://openalex.org/W1612778616","https://openalex.org/W1830783106","https://openalex.org/W1853503627","https://openalex.org/W1975327184","https://openalex.org/W1976343050","https://openalex.org/W1980412136","https://openalex.org/W1990502910","https://openalex.org/W1992867762","https://openalex.org/W1994457272","https://openalex.org/W2002975940","https://openalex.org/W2007980801","https://openalex.org/W2010107360","https://openalex.org/W2026125631","https://openalex.org/W2026391697","https://openalex.org/W2032868343","https://openalex.org/W2033123440","https://openalex.org/W2035808886","https://openalex.org/W2038098381","https://openalex.org/W2044440663","https://openalex.org/W2047028743","https://openalex.org/W2062191306","https://openalex.org/W2078999053","https://openalex.org/W2080025494","https://openalex.org/W2095800140","https://openalex.org/W2106682073","https://openalex.org/W2134308891","https://openalex.org/W2138549733","https://openalex.org/W2148816859","https://openalex.org/W2155552412","https://openalex.org/W2166435158","https://openalex.org/W2208526041","https://openalex.org/W2531495256","https://openalex.org/W2608904218","https://openalex.org/W2906792459","https://openalex.org/W2963561336","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W2909545684","https://openalex.org/W2022608075","https://openalex.org/W613213280","https://openalex.org/W2994889166","https://openalex.org/W3083202704","https://openalex.org/W1998404479","https://openalex.org/W619247846","https://openalex.org/W2992359941","https://openalex.org/W1574084058"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"an":[3],"extended":[4],"version":[5],"of":[6,51],"the":[7,11,16,38],"lecture":[8],"given":[9],"by":[10],"second":[12],"author":[13],"delivered":[14],"at":[15,28],"conference":[17],"\u2018Combinatorics:":[18],"Walter":[19,42],"Deuber":[20],"Memorial":[21],"Meeting\u2019":[22],"held":[23],"on":[24],"7\u20138":[25],"October":[26],"2002":[27],"Humboldt-Universit\u00e4t":[29],"zu":[30],"Berlin.":[31],"Regretfully,":[32],"this":[33,47],"topic":[34],"was":[35],"to":[36],"be":[37],"last":[39],"that":[40],"fascinated":[41],"Deuber's":[43],"mind.":[44],"We":[45],"wrote":[46],"article":[48],"in":[49],"remembrance":[50],"that.":[52]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}