{"id":"https://openalex.org/W2048325184","doi":"https://doi.org/10.1007/s00493-012-2453-1","title":"Projections, entropy and sumsets","display_name":"Projections, entropy and sumsets","publication_year":2012,"publication_date":"2012-03-01","ids":{"openalex":"https://openalex.org/W2048325184","doi":"https://doi.org/10.1007/s00493-012-2453-1","mag":"2048325184"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-012-2453-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-012-2453-1","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/A5003243157","display_name":"Paul Balister","orcid":"https://orcid.org/0000-0003-2696-0352"},"institutions":[{"id":"https://openalex.org/I94658018","display_name":"University of Memphis","ror":"https://ror.org/01cq23130","country_code":"US","type":"education","lineage":["https://openalex.org/I94658018"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul Balister","raw_affiliation_strings":["Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA","University of Memphis, Department of Mathematical Sciences, 38152, Memphis, TN, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA","institution_ids":["https://openalex.org/I94658018"]},{"raw_affiliation_string":"University of Memphis, Department of Mathematical Sciences, 38152, Memphis, TN, USA#TAB#","institution_ids":["https://openalex.org/I94658018"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109915650","display_name":"B\u00e9la Bollob\u00e1s","orcid":"https://orcid.org/0000-0002-9819-7213"},"institutions":[{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"B\u00e9la Bollob\u00e1s","raw_affiliation_strings":["Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, UK","University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, Cambridge, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]},{"raw_affiliation_string":"University of Cambridge, Department of Pure Mathematics and Mathematical Statistics, Cambridge, UK","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109915650"],"corresponding_institution_ids":["https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":5.1839,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.96002334,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"32","issue":"2","first_page":"125","last_page":"141"},"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":0.9997000098228455,"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":0.9997000098228455,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.988099992275238,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/mathematics","display_name":"Mathematics","score":0.8708217740058899},{"id":"https://openalex.org/keywords/inequality","display_name":"Inequality","score":0.655379056930542},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5897760987281799},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.47394800186157227},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46493738889694214},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3916706442832947},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14194801449775696},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11956456303596497}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8708217740058899},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.655379056930542},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5897760987281799},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.47394800186157227},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46493738889694214},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3916706442832947},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14194801449775696},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11956456303596497},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/s00493-012-2453-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-012-2453-1","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":[{"display_name":"Reduced inequalities","score":0.6800000071525574,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W99813126","https://openalex.org/W176241519","https://openalex.org/W572484931","https://openalex.org/W1715489445","https://openalex.org/W1969116803","https://openalex.org/W1993863260","https://openalex.org/W1999339208","https://openalex.org/W2021161286","https://openalex.org/W2024010886","https://openalex.org/W2051793589","https://openalex.org/W2065754663","https://openalex.org/W2073834089","https://openalex.org/W2090322880","https://openalex.org/W2101218996","https://openalex.org/W2105501170","https://openalex.org/W2157827214","https://openalex.org/W2165440928","https://openalex.org/W2608307394","https://openalex.org/W4243521626"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W1991411408","https://openalex.org/W4288278856","https://openalex.org/W2572370460"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
