{"id":"https://openalex.org/W2013408443","doi":"https://doi.org/10.1007/s00493-009-2310-z","title":"On the Fourier spectrum of symmetric Boolean functions","display_name":"On the Fourier spectrum of symmetric Boolean functions","publication_year":2009,"publication_date":"2009-05-01","ids":{"openalex":"https://openalex.org/W2013408443","doi":"https://doi.org/10.1007/s00493-009-2310-z","mag":"2013408443"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-009-2310-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-009-2310-z","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","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/A5037218234","display_name":"Mihail N. Kolountzakis","orcid":"https://orcid.org/0000-0001-9598-4580"},"institutions":[{"id":"https://openalex.org/I142617266","display_name":"University of Crete","ror":"https://ror.org/00dr28g20","country_code":"GR","type":"education","lineage":["https://openalex.org/I142617266"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Mihail N. Kolountzakis","raw_affiliation_strings":["Department of Mathematics, Univ. of Crete, GR-71409, Iraklio, Greece"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Univ. of Crete, GR-71409, Iraklio, Greece","institution_ids":["https://openalex.org/I142617266"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109812838","display_name":"Richard J. Lipton","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I2800444561","display_name":"Atlanta Technical College","ror":"https://ror.org/01s3vfp47","country_code":"US","type":"education","lineage":["https://openalex.org/I2800444561"]},{"id":"https://openalex.org/I2802646204","display_name":"Morristown Medical Center","ror":"https://ror.org/03m6tev69","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2802646204","https://openalex.org/I67339987"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard J. Lipton","raw_affiliation_strings":["Georgia Tech, College of Computing, Atlanta, GA 30332, USA","Telcordia Research, Morristown, NJ, 07960, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Georgia Tech, College of Computing, Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444","https://openalex.org/I2800444561"]},{"raw_affiliation_string":"Telcordia Research, Morristown, NJ, 07960, USA","institution_ids":["https://openalex.org/I2802646204"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009055115","display_name":"Evangelos Markakis","orcid":"https://orcid.org/0000-0003-0959-598X"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Evangelos Markakis","raw_affiliation_strings":["Centre for Math and Computer Science (CWI), Kruislaan 413, Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Math and Computer Science (CWI), Kruislaan 413, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075894805","display_name":"Aranyak Mehta","orcid":"https://orcid.org/0000-0002-6132-4901"},"institutions":[{"id":"https://openalex.org/I4210085935","display_name":"IBM Research - Almaden","ror":"https://ror.org/005w8dd04","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210085935","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Aranyak Mehta","raw_affiliation_strings":["IBM Almaden Research Center, 650 Harry Rd, San Jose, CA, 95120, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Almaden Research Center, 650 Harry Rd, San Jose, CA, 95120, USA","institution_ids":["https://openalex.org/I4210085935"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063089732","display_name":"Nisheeth K. Vishnoi","orcid":"https://orcid.org/0000-0002-0255-1119"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I4210103279","display_name":"IBM Research - India","ror":"https://ror.org/014wt7r80","country_code":"IN","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210103279","https://openalex.org/I4210114115"]}],"countries":["IN","US"],"is_corresponding":false,"raw_author_name":"Nisheeth K. Vishnoi","raw_affiliation_strings":["College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332, USA","IBM India Research Lab, Block-1, IIT Delhi, New Delhi, 110016, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computing, Georgia Institute of Technology, Atlanta, GA, 30332, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"IBM India Research Lab, Block-1, IIT Delhi, New Delhi, 110016, India","institution_ids":["https://openalex.org/I4210103279"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5009055115"],"corresponding_institution_ids":["https://openalex.org/I1341640284"],"apc_list":null,"apc_paid":null,"fwci":2.6169,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.90868801,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"3","first_page":"363","last_page":"387"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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/T11567","display_name":"semigroups and automata theory","score":0.9987000226974487,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9976000189781189,"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/mathematics","display_name":"Mathematics","score":0.869377613067627},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6401854157447815},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.542945146560669},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.5429112911224365},{"id":"https://openalex.org/keywords/symmetric-function","display_name":"Symmetric function","score":0.5312442779541016},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4226084351539612},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15138459205627441},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06569969654083252}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.869377613067627},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6401854157447815},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.542945146560669},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.5429112911224365},{"id":"https://openalex.org/C3746008","wikidata":"https://www.wikidata.org/wiki/Q981351","display_name":"Symmetric function","level":2,"score":0.5312442779541016},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4226084351539612},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15138459205627441},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06569969654083252},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00493-009-2310-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-009-2310-z","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W32262330","https://openalex.org/W169029076","https://openalex.org/W1569556792","https://openalex.org/W1856342626","https://openalex.org/W2002901911","https://openalex.org/W2011618217","https://openalex.org/W2019363670","https://openalex.org/W2040884411","https://openalex.org/W2042194938","https://openalex.org/W2047430378","https://openalex.org/W2073107304","https://openalex.org/W2081585469","https://openalex.org/W2088390444","https://openalex.org/W2108209146","https://openalex.org/W2143724791","https://openalex.org/W2154271831","https://openalex.org/W2276336683","https://openalex.org/W2295021037","https://openalex.org/W3148810677","https://openalex.org/W4205562629","https://openalex.org/W4233039852","https://openalex.org/W4238893454","https://openalex.org/W4249708694","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2092886012","https://openalex.org/W2145874891","https://openalex.org/W2170281757","https://openalex.org/W2119028753","https://openalex.org/W2790802381","https://openalex.org/W2511750106","https://openalex.org/W1982026196","https://openalex.org/W3094037537","https://openalex.org/W3194134751","https://openalex.org/W2151933547"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
