{"id":"https://openalex.org/W2394794047","doi":"https://doi.org/10.4086/toc.2013.v009a029","title":null,"display_name":null,"publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2394794047","doi":"https://doi.org/10.4086/toc.2013.v009a029","mag":"2394794047"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2013.v009a029","pdf_url":"https://theoryofcomputing.org/articles/v009a029/v009a029.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://theoryofcomputing.org/articles/v009a029/v009a029.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000042413","display_name":"Eric Blais","orcid":"https://orcid.org/0009-0000-5824-9034"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eric Blais","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029451171","display_name":"Li-Yang Tan","orcid":"https://orcid.org/0000-0002-1279-4384"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li-Yang Tan","raw_affiliation_strings":[],"affiliations":[]}],"institution_assertions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.285,"has_fulltext":true,"fulltext_origin":"pdf","cited_by_count":5,"citation_normalized_percentile":{"value":0.706021,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":80,"max":81},"biblio":{"volume":"9","issue":"1","first_page":"889","last_page":"896"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9996,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9981,"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/lemma","display_name":"Lemma (botany)","score":0.6616902},{"id":"https://openalex.org/keywords/statement","display_name":"Statement (logic)","score":0.55406827}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.824576},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6616902},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6288211},{"id":"https://openalex.org/C2777026412","wikidata":"https://www.wikidata.org/wiki/Q2684591","display_name":"Statement (logic)","level":2,"score":0.55406827},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46198234},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.4354021},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06633723},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2013.v009a029","pdf_url":"https://theoryofcomputing.org/articles/v009a029/v009a029.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2013.v009a029","pdf_url":"https://theoryofcomputing.org/articles/v009a029/v009a029.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.53,"id":"https://metadata.un.org/sdg/10"}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":23,"referenced_works":["https://openalex.org/W1559492868","https://openalex.org/W1571037334","https://openalex.org/W1886650756","https://openalex.org/W1978526953","https://openalex.org/W1986296546","https://openalex.org/W2005090831","https://openalex.org/W2019121884","https://openalex.org/W2028932986","https://openalex.org/W2029370139","https://openalex.org/W2057463449","https://openalex.org/W2058422149","https://openalex.org/W2073310493","https://openalex.org/W2078929687","https://openalex.org/W2080233228","https://openalex.org/W2080479164","https://openalex.org/W2087038607","https://openalex.org/W2099111195","https://openalex.org/W2103749128","https://openalex.org/W2327680971","https://openalex.org/W2465088004","https://openalex.org/W2742022539","https://openalex.org/W2885803187","https://openalex.org/W4226347946"],"related_works":["https://openalex.org/W4308265086","https://openalex.org/W3168772390","https://openalex.org/W3006682748","https://openalex.org/W2949964783","https://openalex.org/W2801357573","https://openalex.org/W2768610039","https://openalex.org/W2735923117","https://openalex.org/W2115913661","https://openalex.org/W2106889256","https://openalex.org/W1097487277"],"abstract_inverted_index":{"$":[0,3,68,77],"\\newcommand{\\R}{{\\mathbb":[1],"R}}":[2],"The":[4,46],"Hypercontractive":[5,66,127],"Inequality":[6,67,128],"of":[7,33,49,62,118],"Bonami":[8],"(1968,":[9],"1970)":[10],"and":[11,25,55,84,99,112],"Gross":[12],"(1975)":[13],"is":[14,52],"equivalent":[15],"to":[16,103,123],"the":[17,63,89,105,116,125],"following":[18],"statement:":[19],"for":[20,129],"every":[21,26],"$q":[22],">":[23],"2$":[24],"function":[27],"$f":[28],":":[29],"\\{-1,1\\}^n":[30],"\\to":[31],"\\R$":[32],"Fourier":[34],"degree":[35],"at":[36],"most":[37],"$m$,":[38],"$$":[39,45],"\\|f":[40],"\\|_q":[41],"\\le":[42,72],"(q-1)^{m/2}":[43],"\\|f\\|_2.":[44],"original":[47],"proof":[48,61],"this":[50],"inequality":[51],"analytical.":[53],"Friedgut":[54],"R\u00f6dl":[56],"(2001)":[57],"gave":[58],"an":[59],"alternative":[60],"slightly":[64],"weaker":[65],"\\|":[69,74],"f":[70,75],"\\|_4":[71],"28^{m/4}":[73],"\\|_2":[76],"by":[78],"combining":[79],"tools":[80],"from":[81],"information":[82],"theory":[83],"combinatorics.":[85],"Specifically,":[86],"they":[87],"recast":[88],"problem":[90],"as":[91],"a":[92],"statement":[93],"about":[94,115],"multi-hypergraphs,":[95],"generalized":[96],"Shearer's":[97,110],"lemma,":[98],"used":[100],"probabilistic":[101],"arguments":[102,114],"obtain":[104],"inequality.":[106],"We":[107],"show":[108],"that":[109],"Lemma":[111],"elementary":[113],"entropy":[117],"random":[119],"variables":[120],"are":[121],"sufficient":[122],"recover":[124],"optimal":[126],"all":[130],"even":[131],"integers":[132],"$q$.":[133]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2394794047","counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-03-20T15:38:57.421643","created_date":"2016-06-24"}