{"id":"https://openalex.org/W2617565733","doi":"https://doi.org/10.37236/7042","title":"Convolution Estimates and Number of Disjoint Partitions","display_name":"Convolution Estimates and Number of Disjoint Partitions","publication_year":2017,"publication_date":"2017-06-30","ids":{"openalex":"https://openalex.org/W2617565733","doi":"https://doi.org/10.37236/7042","mag":"2617565733"},"language":"en","primary_location":{"id":"doi:10.37236/7042","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7042","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/7042","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033685269","display_name":"Paata Ivanisvili","orcid":null},"institutions":[{"id":"https://openalex.org/I149910238","display_name":"Kent State University","ror":"https://ror.org/049pfb863","country_code":"US","type":"education","lineage":["https://openalex.org/I149910238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paata Ivanisvili","raw_affiliation_strings":["Kent State University"],"affiliations":[{"raw_affiliation_string":"Kent State University","institution_ids":["https://openalex.org/I149910238"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033685269"],"corresponding_institution_ids":["https://openalex.org/I149910238"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.152019,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"24","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9894000291824341,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T12508","display_name":"Functional Equations Stability Results","score":0.9801999926567078,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.8889265060424805},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7308706045150757},{"id":"https://openalex.org/keywords/disjoint-union","display_name":"Disjoint union (topology)","score":0.715475857257843},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.6687644720077515},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.626718282699585},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5934026837348938},{"id":"https://openalex.org/keywords/approx","display_name":"Approx","score":0.5051937699317932},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3881515860557556},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13576951622962952},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10984957218170166}],"concepts":[{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.8889265060424805},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7308706045150757},{"id":"https://openalex.org/C7655956","wikidata":"https://www.wikidata.org/wiki/Q5282259","display_name":"Disjoint union (topology)","level":2,"score":0.715475857257843},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.6687644720077515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.626718282699585},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5934026837348938},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.5051937699317932},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3881515860557556},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13576951622962952},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10984957218170166},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/7042","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7042","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1705.08529","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1705.08529","pdf_url":"https://arxiv.org/pdf/1705.08529","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2617565733","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1705.08529.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1705.08529","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1705.08529","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/7042","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7042","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2514589972","https://openalex.org/W2587498643"],"related_works":["https://openalex.org/W2154543259","https://openalex.org/W2023903399","https://openalex.org/W1483904091","https://openalex.org/W2953585012","https://openalex.org/W2949155560","https://openalex.org/W1999312242","https://openalex.org/W2072556229","https://openalex.org/W72163051","https://openalex.org/W2901141289","https://openalex.org/W2560768522","https://openalex.org/W2950388741","https://openalex.org/W2949635812","https://openalex.org/W2519749115","https://openalex.org/W1976681187","https://openalex.org/W1996363709","https://openalex.org/W43828175","https://openalex.org/W3038113379","https://openalex.org/W2802729448","https://openalex.org/W2310381493","https://openalex.org/W3106160126"],"abstract_inverted_index":{"Let":[0],"$X$":[1,21],"be":[2],"a":[3,14,23],"finite":[4,58],"collection":[5],"of":[6,12,17,45,60],"sets.":[7],"We":[8],"count":[9],"the":[10,29,42,49],"number":[11,30,59],"ways":[13],"disjoint":[15,61],"union":[16],"$n-1$":[18,62],"subsets":[19],"in":[20,25],"is":[22],"set":[24],"$X$,":[26],"and":[27],"estimate":[28],"from":[31],"above":[32],"by":[33],"$|X|^{c(n)}$":[34],"where":[35,52],"$$c(n)=\\left(1-\\frac{(n-1)\\ln":[36],"(n-1)}{n\\ln":[37],"n}":[38],"\\right)^{-1}.$$":[39],"This":[40],"extends":[41],"recent":[43],"result":[44],"Kane-Tao,":[46],"corresponding":[47],"to":[48,55],"case":[50],"$n=3$":[51],"$c(3)\\approx":[53],"1.725$,":[54],"an":[56],"arbitrary":[57],"partitions.":[63]},"counts_by_year":[],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2025-10-10T00:00:00"}