{"id":"https://openalex.org/W2122166315","doi":"https://doi.org/10.1002/rsa.3240060111","title":"Fractional products of sets","display_name":"Fractional products of sets","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W2122166315","doi":"https://doi.org/10.1002/rsa.3240060111","mag":"2122166315"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.3240060111","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240060111","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures &amp; Algorithms","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/A5026614598","display_name":"Ron C. Blei","orcid":null},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ron Blei","raw_affiliation_strings":["Department of Mathematics, University of Connecticut, Storrs, CT 06269","Department of Mathematics , University of Connecticut , Storrs, CT, 06269"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Connecticut, Storrs, CT 06269","institution_ids":["https://openalex.org/I140172145"]},{"raw_affiliation_string":"Department of Mathematics , University of Connecticut , Storrs, CT, 06269","institution_ids":["https://openalex.org/I140172145"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020836845","display_name":"Yuval Peres","orcid":"https://orcid.org/0000-0001-5456-6323"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuval Peres","raw_affiliation_strings":["Department of Statistics, University of California, Berkeley, CA 94720","Department of Statistics, University of California, Berkeley, CA 94720;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of California, Berkeley, CA 94720","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"Department of Statistics, University of California, Berkeley, CA 94720;","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091663311","display_name":"James H. Schmerl","orcid":"https://orcid.org/0000-0003-0545-8339"},"institutions":[{"id":"https://openalex.org/I140172145","display_name":"University of Connecticut","ror":"https://ror.org/02der9h97","country_code":"US","type":"education","lineage":["https://openalex.org/I140172145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Schmerl","raw_affiliation_strings":["Department of Mathematics, University of Connecticut, Storrs, CT 06269","Department of Mathematics , University of Connecticut , Storrs, CT, 06269"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Connecticut, Storrs, CT 06269","institution_ids":["https://openalex.org/I140172145"]},{"raw_affiliation_string":"Department of Mathematics , University of Connecticut , Storrs, CT, 06269","institution_ids":["https://openalex.org/I140172145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.27329193,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"6","issue":"1","first_page":"113","last_page":"119"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11476","display_name":"Graph theory and applications","score":0.9923999905586243,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.9921000003814697,"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/cartesian-product","display_name":"Cartesian product","score":0.9012795686721802},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6459382176399231},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6061998009681702},{"id":"https://openalex.org/keywords/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.5613754391670227},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47190600633621216},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4058288037776947},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3206692337989807},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2552974224090576},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13236746191978455},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11816781759262085}],"concepts":[{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.9012795686721802},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6459382176399231},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6061998009681702},{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.5613754391670227},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47190600633621216},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4058288037776947},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3206692337989807},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2552974224090576},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13236746191978455},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11816781759262085}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/rsa.3240060111","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.3240060111","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures &amp; Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1495591881","https://openalex.org/W1968454212","https://openalex.org/W2009852526","https://openalex.org/W2021022635","https://openalex.org/W2052568920","https://openalex.org/W2076176821","https://openalex.org/W2312528841","https://openalex.org/W2334724020","https://openalex.org/W4236473834"],"related_works":["https://openalex.org/W2949097972","https://openalex.org/W4299640900","https://openalex.org/W2141418112","https://openalex.org/W3163064202","https://openalex.org/W2738565459","https://openalex.org/W3159629589","https://openalex.org/W2601112296","https://openalex.org/W2131259888","https://openalex.org/W3030274415","https://openalex.org/W68628300"],"abstract_inverted_index":{"Abstract":[0],"For":[1],"integers":[2],"d":[3,16],"&gt;":[4],"1":[5,8],"and":[6],"arbitrary":[7],"\u2a7d":[9,11],"\u03b1":[10,13],"d,":[12],"\u2010products":[14],"in":[15],"\u2010fold":[17],"Cartesian":[18],"products":[19],"are":[20,28],"produced":[21],"by":[22,30],"probabilistic":[23],"methods.":[24],"Some":[25],"explicit":[26],"constructions":[27],"given":[29],"solutions":[31],"of":[32,34],"instances":[33],"the":[35],"Tur\u00e1n":[36],"problem":[37],"for":[38],"graphs.":[39]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
