{"id":"https://openalex.org/W2127754540","doi":"https://doi.org/10.1017/s0963548307008413","title":"On Cancellative Set Families","display_name":"On Cancellative Set Families","publication_year":2007,"publication_date":"2007-02-21","ids":{"openalex":"https://openalex.org/W2127754540","doi":"https://doi.org/10.1017/s0963548307008413","mag":"2127754540"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548307008413","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548307008413","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-00681899","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081660521","display_name":"J\u00e1nos K\u00f6rner","orcid":"https://orcid.org/0000-0003-0546-451X"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"J\u00c1NOS K\u00d6RNER","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 \u2018La Sapienza\u2019, via Salaria 113, 00198 Roma, Italy (e-mail:","Universita degli Studi di Roma La Sapienza, Rome"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 \u2018La Sapienza\u2019, via Salaria 113, 00198 Roma, Italy (e-mail:","institution_ids":["https://openalex.org/I861853513"]},{"raw_affiliation_string":"Universita degli Studi di Roma La Sapienza, Rome","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027309652","display_name":"Blerina Sinaimeri","orcid":"https://orcid.org/0000-0002-9797-7592"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"BLERINA SINAIMERI","raw_affiliation_strings":["Department of Computer Science, Universit\u00e0 \u2018La Sapienza\u2019, via Salaria 113, 00198 Roma, Italy (e-mail:","University of Rome \u201cLa Sapienza \u201d"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Universit\u00e0 \u2018La Sapienza\u2019, via Salaria 113, 00198 Roma, Italy (e-mail:","institution_ids":["https://openalex.org/I861853513"]},{"raw_affiliation_string":"University of Rome \u201cLa Sapienza \u201d","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5081660521"],"corresponding_institution_ids":["https://openalex.org/I861853513"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.15471746,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"5","first_page":"767","last_page":"773"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5559468865394592},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3424089848995209},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.24094024300575256}],"concepts":[{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5559468865394592},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3424089848995209},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.24094024300575256},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548307008413","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548307008413","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:HAL:hal-00681899v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00681899","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics, Probability and Computing, 2007, 16 (5), pp.767-773. &#x27E8;10.1017/S0963548307008413&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:iris.luiss.it:11385/202519","is_oa":false,"landing_page_url":"http://hdl.handle.net/11385/202519","pdf_url":null,"source":{"id":"https://openalex.org/S4377196446","display_name":"IRIS - Institutional Research Information System (Libera Universit\u00e0 Internazionale degli Studi Sociali Guido Carli)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I56441308","host_organization_name":"Libera Universit\u00e0 Internazionale degli Studi Sociali Guido Carli","host_organization_lineage":["https://openalex.org/I56441308"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.uniroma1.it:11573/363003","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/363003","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00681899v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00681899","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics, Probability and Computing, 2007, 16 (5), pp.767-773. &#x27E8;10.1017/S0963548307008413&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1531592115","https://openalex.org/W1549664537","https://openalex.org/W2012584108","https://openalex.org/W2013108310","https://openalex.org/W2023678139","https://openalex.org/W2106100363","https://openalex.org/W2146586570"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"A":[0,15,26,32,55,59,63],"family":[1],"of":[2,4,23,46,72,76,79,81,98,105],"subsets":[3,80],"an":[5,82],"n":[6,83,108,112],"-set":[7,84],"is":[8,85],"2-cancellative":[9,99],"if,":[10],"for":[11,62],"every":[12],"four-tuple":[13],"{":[14],",":[16,18,20,64,66],"B":[17,28,34,57,65],"C":[19,30,38,61,67],"D":[21,36,40],"}":[22],"its":[24],"members,":[25],"\u222a":[27,29,33,35,56,60],"=":[31,39],"implies":[37],".":[41,113],"This":[42],"generalizes":[43],"the":[44,52,73,96,102],"concept":[45],"cancellative":[47,77],"set":[48],"families,":[49,100],"defined":[50],"by":[51],"property":[53],"that":[54],"\u2260":[58],"all":[68],"different.":[69],"The":[70],"asymptotics":[71],"maximum":[74],"size":[75,97],"families":[78],"known":[86],"(Tolhuizen":[87],"[7]).":[88],"We":[89],"provide":[90],"a":[91],"new":[92],"upper":[93],"bound":[94,104],"on":[95],"improving":[101],"previous":[103],"2":[106,110],"0.458":[107],"to":[109],"0.42":[111]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
