{"id":"https://openalex.org/W2086861401","doi":"https://doi.org/10.1137/080717286","title":"On Additive Doubling and Energy","display_name":"On Additive Doubling and Energy","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2086861401","doi":"https://doi.org/10.1137/080717286","mag":"2086861401"},"language":"en","primary_location":{"id":"doi:10.1137/080717286","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080717286","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5111507812","display_name":"Nets Hawk Katz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nets Hawk Katz","raw_affiliation_strings":["nhkatz@indiana.edu and paulhkoester@gmail.com#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"nhkatz@indiana.edu and paulhkoester@gmail.com#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050203012","display_name":"Paul Koester","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul Koester","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.4297,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.99107143,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"24","issue":"4","first_page":"1684","last_page":"1693"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9871000051498413,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9735000133514404,"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/conjecture","display_name":"Conjecture","score":0.7842025756835938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.772555947303772},{"id":"https://openalex.org/keywords/subtractive-color","display_name":"Subtractive color","score":0.6826567649841309},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6299057602882385},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6047014594078064},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5872264504432678},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5676578879356384},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4996929168701172},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4675625264644623},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4434836804866791},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12424907088279724},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08271464705467224},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08230507373809814},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0638570785522461}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7842025756835938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.772555947303772},{"id":"https://openalex.org/C150799807","wikidata":"https://www.wikidata.org/wiki/Q374081","display_name":"Subtractive color","level":2,"score":0.6826567649841309},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6299057602882385},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6047014594078064},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5872264504432678},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5676578879356384},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4996929168701172},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4675625264644623},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4434836804866791},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12424907088279724},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08271464705467224},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08230507373809814},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0638570785522461},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080717286","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080717286","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.243.1054","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.243.1054","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0802.4371v1.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.49000000953674316}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1555768633","https://openalex.org/W2106474499","https://openalex.org/W2152351539","https://openalex.org/W2951918178"],"related_works":["https://openalex.org/W1529715114","https://openalex.org/W1978042415","https://openalex.org/W1562041956","https://openalex.org/W1975966127","https://openalex.org/W3038654277","https://openalex.org/W2962878639","https://openalex.org/W1575039872","https://openalex.org/W4294608140","https://openalex.org/W2740334431","https://openalex.org/W4212808623"],"abstract_inverted_index":{"We":[0,10],"discuss":[1],"some":[2],"ideas":[3],"related":[4,33],"to":[5,34],"the":[6,46,51,83],"polynomial":[7,52],"Freiman\u2013Ruzsa":[8,53],"conjecture.":[9],"show":[11],"that":[12,19,45,64],"there":[13],"is":[14,61,71],"a":[15,35,72],"universal":[16],"$\\epsilon>0$":[17],"so":[18],"any":[20],"subset":[21],"of":[22,56,76],"an":[23],"abelian":[24],"group":[25],"with":[26,37],"subtractive":[27],"doubling":[28],"K":[29],"must":[30],"be":[31],"polynomially":[32],"set":[36],"additive":[38],"energy":[39,60],"at":[40],"least":[41],"$\\frac{1}{K^{1-\\epsilon}}$.":[42],"This":[43],"means":[44],"main":[47],"difficulty":[48],"in":[49,82],"proving":[50],"conjecture":[54],"consists":[55],"studying":[57],"sets":[58],"whose":[59],"greater":[62],"than":[63],"implied":[65],"by":[66],"their":[67],"doubling.":[68],"One":[69],"example":[70],"generalized":[73],"arithmetic":[74],"progression":[75],"high":[77],"dimension":[78],"which":[79],"cannot":[80],"occur":[81],"finite":[84],"characteristic":[85],"setting.":[86]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":9}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2025-10-10T00:00:00"}
