{"id":"https://openalex.org/W2111478028","doi":"https://doi.org/10.1145/1374376.1374454","title":"Inverse conjecture for the gowers norm is false","display_name":"Inverse conjecture for the gowers norm is false","publication_year":2008,"publication_date":"2008-05-17","ids":{"openalex":"https://openalex.org/W2111478028","doi":"https://doi.org/10.1145/1374376.1374454","mag":"2111478028"},"language":"en","primary_location":{"id":"doi:10.1145/1374376.1374454","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1374376.1374454","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the fortieth annual ACM symposium on Theory of computing","raw_type":"proceedings-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/A5044999305","display_name":"Shachar Lovett","orcid":"https://orcid.org/0000-0003-4552-1443"},"institutions":[{"id":"https://openalex.org/I53964585","display_name":"Weizmann Institute of Science","ror":"https://ror.org/0316ej306","country_code":"IL","type":"education","lineage":["https://openalex.org/I53964585"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shachar Lovett","raw_affiliation_strings":["The Weizmann Institute of Science, Rehovot, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Weizmann Institute of Science, Rehovot, Israel","institution_ids":["https://openalex.org/I53964585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059452045","display_name":"Roy Meshulam","orcid":"https://orcid.org/0000-0003-3804-4300"},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Roy Meshulam","raw_affiliation_strings":["The Technion, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Technion, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004360801","display_name":"Alex Samorodnitsky","orcid":"https://orcid.org/0000-0001-8643-7948"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Alex Samorodnitsky","raw_affiliation_strings":["The Hebrew University in Jerusalem, Jerusalem, Israel","The Hebrew University in Jerusalem, Jerusalem, Israel#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Hebrew University in Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]},{"raw_affiliation_string":"The Hebrew University in Jerusalem, Jerusalem, Israel#TAB#","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":14.7994,"has_fulltext":false,"cited_by_count":45,"citation_normalized_percentile":{"value":0.99460432,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"547","last_page":"556"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T10374","display_name":"Advanced Graph Theory Research","score":0.9986000061035156,"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/conjecture","display_name":"Conjecture","score":0.6121309995651245},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.6119090914726257},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4942655563354492},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4934791326522827},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3830224871635437},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32546740770339966},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.10820642113685608}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6121309995651245},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.6119090914726257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4942655563354492},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4934791326522827},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3830224871635437},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32546740770339966},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.10820642113685608},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1374376.1374454","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1374376.1374454","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the fortieth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1554682571","https://openalex.org/W1585475679","https://openalex.org/W1606480398","https://openalex.org/W1970630090","https://openalex.org/W1997855358","https://openalex.org/W2014997928","https://openalex.org/W2064334110","https://openalex.org/W2080132708","https://openalex.org/W2129107602","https://openalex.org/W2138852390","https://openalex.org/W2141304880","https://openalex.org/W2155600383","https://openalex.org/W2157443379","https://openalex.org/W2190698610","https://openalex.org/W2335400162","https://openalex.org/W2949694092","https://openalex.org/W2963585281","https://openalex.org/W3004537778","https://openalex.org/W3151527484"],"related_works":["https://openalex.org/W2119971017","https://openalex.org/W2748800470","https://openalex.org/W2029981401","https://openalex.org/W2949426312","https://openalex.org/W2740334431","https://openalex.org/W4212808623","https://openalex.org/W4301344670","https://openalex.org/W2951982256","https://openalex.org/W2057801831","https://openalex.org/W2013467167"],"abstract_inverted_index":{"Let":[0],"p":[1],"be":[2,9,76,164],"a":[3,10,28,39,47,51,125,128,147],"fixed":[4],"prime":[5,66,168],"number":[6],"and":[7,63,80,120,133,157],"N":[8],"large":[11],"integer.":[12],"The":[13,55],"\"Inverse":[14],"Conjecture":[15],"for":[16,61,64,78,81,113,166,170],"the":[17,23,73,107,153,160],"Gowers":[18,25,90],"Norm\"":[19],"states":[20],"that":[21,35,146],"if":[22],"\"d-th":[24],"norm\"":[26],"of":[27,42,100,127,131,138,149,155],"function":[29,87],"f:FNp":[30],"to":[31,59,75,135,163],"Fp":[32],"is":[33,36,57,92,103],"non-negligible,":[34,93],"larger":[37],"than":[38],"constant":[40],"independent":[41],"N,":[43],"then":[44],"f":[45],"has":[46],"non-trivial":[48],"correlation":[49,96],"with":[50,97,110,152],"degree":[52,101],"d-1":[53],"polynomial.":[54],"conjecture":[56,74,162],"known":[58],"hold":[60],"d=2,3":[62],"any":[65,98,167],"p.":[67],"In":[68],"this":[69],"paper":[70],"we":[71],"show":[72,136],"false":[77,165],"p=2":[79],"d=4,":[82],"by":[83,118,141],"presenting":[84],"an":[85],"explicit":[86],"whose":[88,95],"4-th":[89],"norm":[91],"but":[94],"polynomial":[99],"3":[102],"exponentially":[104],"small.":[105],"Essentially":[106],"same":[108],"result,":[109],"different":[111],"bounds":[112],"correlation,":[114],"was":[115],"independently":[116],"obtained":[117],"Green":[119],"Tao.":[121],"Their":[122],"analysis":[123],"uses":[124],"modification":[126],"Ramsey-type":[129],"argument":[130,154],"Alon":[132,156],"Beigel":[134,158],"inapproximability":[137],"certain":[139],"functions":[140],"low-degree":[142],"polynomials.":[143],"We":[144],"observe":[145],"combination":[148],"our":[150],"results":[151],"implies":[159],"inverse":[161],"p,":[169],"d":[171],"=":[172],"p2.":[173]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
