{"id":"https://openalex.org/W1985076392","doi":"https://doi.org/10.1016/0166-218x(91)90032-r","title":"The threshold order of a Boolean function","display_name":"The threshold order of a Boolean function","publication_year":1991,"publication_date":"1991-03-01","ids":{"openalex":"https://openalex.org/W1985076392","doi":"https://doi.org/10.1016/0166-218x(91)90032-r","mag":"1985076392"},"language":"en","primary_location":{"id":"doi:10.1016/0166-218x(91)90032-r","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0166-218x(91)90032-r","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","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/A5100342202","display_name":"Chi Wang","orcid":"https://orcid.org/0000-0001-5610-5547"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Chi Wang","raw_affiliation_strings":["RUTCOR, Hill Center, Busch Campus, Rutgers University, New Brunswick, NJ 08903, USA"],"affiliations":[{"raw_affiliation_string":"RUTCOR, Hill Center, Busch Campus, Rutgers University, New Brunswick, NJ 08903, USA","institution_ids":["https://openalex.org/I102322142"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072551968","display_name":"Adrian Williams","orcid":"https://orcid.org/0000-0003-2098-808X"},"institutions":[{"id":"https://openalex.org/I102322142","display_name":"Rutgers, The State University of New Jersey","ror":"https://ror.org/05vt9qd57","country_code":"US","type":"education","lineage":["https://openalex.org/I102322142"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A.C. Williams","raw_affiliation_strings":["RUTCOR, Hill Center, Busch Campus, Rutgers University, New Brunswick, NJ 08903, USA"],"affiliations":[{"raw_affiliation_string":"RUTCOR, Hill Center, Busch Campus, Rutgers University, New Brunswick, NJ 08903, USA","institution_ids":["https://openalex.org/I102322142"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100342202"],"corresponding_institution_ids":["https://openalex.org/I102322142"],"apc_list":{"value":2750,"currency":"USD","value_usd":2750},"apc_paid":null,"fwci":2.6917,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.90224763,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"31","issue":"1","first_page":"51","last_page":"69"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9896000027656555,"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"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9896000027656555,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9835000038146973,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9829000234603882,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.845623254776001},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8139918446540833},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.6923083066940308},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6434774398803711},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5997660756111145},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5227009057998657},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5036858916282654},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.48254626989364624},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.4748166799545288},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.46181073784828186},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45138341188430786},{"id":"https://openalex.org/keywords/boolean-network","display_name":"Boolean network","score":0.44216811656951904},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1388351321220398}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.845623254776001},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8139918446540833},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.6923083066940308},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6434774398803711},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5997660756111145},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5227009057998657},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5036858916282654},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48254626989364624},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.4748166799545288},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.46181073784828186},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45138341188430786},{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.44216811656951904},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1388351321220398},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0166-218x(91)90032-r","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0166-218x(91)90032-r","pdf_url":null,"source":{"id":"https://openalex.org/S171741597","display_name":"Discrete Applied Mathematics","issn_l":"0166-218X","issn":["0166-218X","1872-6771"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Applied Mathematics","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":17,"referenced_works":["https://openalex.org/W1609370892","https://openalex.org/W1662824729","https://openalex.org/W1799057383","https://openalex.org/W1969423858","https://openalex.org/W1980985059","https://openalex.org/W1994799860","https://openalex.org/W2011039300","https://openalex.org/W2041273777","https://openalex.org/W2041698105","https://openalex.org/W2295866677","https://openalex.org/W2314893179","https://openalex.org/W2496493191","https://openalex.org/W2587987525","https://openalex.org/W4210783262","https://openalex.org/W6646552618","https://openalex.org/W6660455021","https://openalex.org/W6723885470"],"related_works":["https://openalex.org/W2106622045","https://openalex.org/W4252281389","https://openalex.org/W1991822629","https://openalex.org/W2011902727","https://openalex.org/W2011175857","https://openalex.org/W3141532631","https://openalex.org/W2061512596","https://openalex.org/W2105128170","https://openalex.org/W2131164334","https://openalex.org/W2918709778"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
