{"id":"https://openalex.org/W1510995219","doi":"https://doi.org/10.1017/s0963548316000432","title":"An Inequality for Functions on the Hamming Cube","display_name":"An Inequality for Functions on the Hamming Cube","publication_year":2017,"publication_date":"2017-03-29","ids":{"openalex":"https://openalex.org/W1510995219","doi":"https://doi.org/10.1017/s0963548316000432","mag":"1510995219"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548316000432","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548316000432","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3770E7921E125EF4A73A413E396348CB/S0963548316000432a.pdf/div-class-title-an-inequality-for-functions-on-the-hamming-cube-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3770E7921E125EF4A73A413E396348CB/S0963548316000432a.pdf/div-class-title-an-inequality-for-functions-on-the-hamming-cube-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":true,"raw_author_name":"ALEX SAMORODNITSKY","raw_affiliation_strings":["School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail:"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering and Computer Science, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (e-mail:","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5004360801"],"corresponding_institution_ids":["https://openalex.org/I197251160"],"apc_list":null,"apc_paid":null,"fwci":0.7184,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72479689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"26","issue":"3","first_page":"468","last_page":"480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9975000023841858,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/isoperimetric-inequality","display_name":"Isoperimetric inequality","score":0.9115703105926514},{"id":"https://openalex.org/keywords/cube","display_name":"Cube (algebra)","score":0.878549337387085},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.7201332449913025},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6538363099098206},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.6212249994277954},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.5520039200782776},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5483849048614502},{"id":"https://openalex.org/keywords/isoperimetric-dimension","display_name":"Isoperimetric dimension","score":0.5191246867179871},{"id":"https://openalex.org/keywords/rearrangement-inequality","display_name":"Rearrangement inequality","score":0.4568125009536743},{"id":"https://openalex.org/keywords/log-sum-inequality","display_name":"Log sum inequality","score":0.4156157970428467},{"id":"https://openalex.org/keywords/unit-cube","display_name":"Unit cube","score":0.4130955934524536},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3536854088306427},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2264024019241333},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10786363482475281}],"concepts":[{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.9115703105926514},{"id":"https://openalex.org/C53051483","wikidata":"https://www.wikidata.org/wiki/Q861555","display_name":"Cube (algebra)","level":2,"score":0.878549337387085},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.7201332449913025},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6538363099098206},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.6212249994277954},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.5520039200782776},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5483849048614502},{"id":"https://openalex.org/C70266181","wikidata":"https://www.wikidata.org/wiki/Q3707726","display_name":"Isoperimetric dimension","level":3,"score":0.5191246867179871},{"id":"https://openalex.org/C126087398","wikidata":"https://www.wikidata.org/wiki/Q1149189","display_name":"Rearrangement inequality","level":4,"score":0.4568125009536743},{"id":"https://openalex.org/C46979015","wikidata":"https://www.wikidata.org/wiki/Q6666859","display_name":"Log sum inequality","level":3,"score":0.4156157970428467},{"id":"https://openalex.org/C60432849","wikidata":"https://www.wikidata.org/wiki/Q2072112","display_name":"Unit cube","level":2,"score":0.4130955934524536},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3536854088306427},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2264024019241333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10786363482475281},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548316000432","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548316000432","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3770E7921E125EF4A73A413E396348CB/S0963548316000432a.pdf/div-class-title-an-inequality-for-functions-on-the-hamming-cube-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1207.1233","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1207.1233","pdf_url":"https://arxiv.org/pdf/1207.1233","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:1510995219","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1207.1233","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1207.1233","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1207.1233","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1017/s0963548316000432","is_oa":true,"landing_page_url":"https://doi.org/10.1017/s0963548316000432","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/3770E7921E125EF4A73A413E396348CB/S0963548316000432a.pdf/div-class-title-an-inequality-for-functions-on-the-hamming-cube-div.pdf","source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5799999833106995,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G2894355452","display_name":null,"funder_award_id":"1241/11","funder_id":"https://openalex.org/F4320322252","funder_display_name":"Israel Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1510995219.pdf","grobid_xml":"https://content.openalex.org/works/W1510995219.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W97263645","https://openalex.org/W634962210","https://openalex.org/W1871596124","https://openalex.org/W1990331975","https://openalex.org/W2007029088","https://openalex.org/W2081052144","https://openalex.org/W2120997209","https://openalex.org/W2130523901","https://openalex.org/W2327680971","https://openalex.org/W4212998659","https://openalex.org/W4235805661"],"related_works":["https://openalex.org/W2962741170","https://openalex.org/W2071763320","https://openalex.org/W2005838725","https://openalex.org/W2111185360","https://openalex.org/W3201584881","https://openalex.org/W2575715081","https://openalex.org/W2113616621","https://openalex.org/W2610710049","https://openalex.org/W3035097110","https://openalex.org/W2012119535","https://openalex.org/W2225806586","https://openalex.org/W3195149909","https://openalex.org/W2952441060","https://openalex.org/W2277096349","https://openalex.org/W976371925","https://openalex.org/W3086724848","https://openalex.org/W2136340307","https://openalex.org/W2091373828","https://openalex.org/W2580831367","https://openalex.org/W1551519020"],"abstract_inverted_index":{"We":[0],"prove":[1],"an":[2],"inequality":[3,16,20],"for":[4,17],"functions":[5],"on":[6,33],"the":[7,14,27,34,46,49],"discrete":[8],"cube":[9,47],"{0,":[10],"1}":[11],"n":[12],"extending":[13],"edge-isoperimetric":[15],"sets.":[18],"This":[19],"turns":[21],"out":[22],"to":[23,26],"be":[24],"equivalent":[25],"following":[28],"claim":[29],"about":[30],"random":[31],"walks":[32],"cube:":[35],"subcubes":[36],"maximize":[37],"\u2018mean":[38],"first":[39],"exit":[40],"time\u2019":[41],"among":[42],"all":[43],"subsets":[44],"of":[45,48],"same":[50],"cardinality.":[51]},"counts_by_year":[{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}