{"id":"https://openalex.org/W2146275066","doi":"https://doi.org/10.1017/s0963548312000168","title":"<i>k</i>-Sums in Abelian Groups","display_name":"<i>k</i>-Sums in Abelian Groups","publication_year":2012,"publication_date":"2012-04-23","ids":{"openalex":"https://openalex.org/W2146275066","doi":"https://doi.org/10.1017/s0963548312000168","mag":"2146275066"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548312000168","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548312000168","pdf_url":null,"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":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1110.1961","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020345400","display_name":"Benjamin Girard","orcid":null},"institutions":[{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"BENJAMIN GIRARD","raw_affiliation_strings":["IMJ, \u00c9quipe Combinatoire et Optimisation, Universit\u00e9 Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75005 Paris, France (e-mail:","IMJ - Institut de Math\u00e9matiques de Jussieu (2, place Jussieu 75251 Paris Cedex 05 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMJ, \u00c9quipe Combinatoire et Optimisation, Universit\u00e9 Pierre et Marie Curie (Paris 6), 4 Place Jussieu, 75005 Paris, France (e-mail:","institution_ids":["https://openalex.org/I39804081"]},{"raw_affiliation_string":"IMJ - Institut de Math\u00e9matiques de Jussieu (2, place Jussieu 75251 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I3017942884"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077696461","display_name":"Simon Griffiths","orcid":"https://orcid.org/0000-0003-2435-7963"},"institutions":[{"id":"https://openalex.org/I141883831","display_name":"Instituto Nacional de Matem\u00e1tica Pura e Aplicada","ror":"https://ror.org/028caqe42","country_code":"BR","type":"facility","lineage":["https://openalex.org/I141883831","https://openalex.org/I4210151455"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"SIMON GRIFFITHS","raw_affiliation_strings":["IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brasil 22460-320 (e-mail:","IMPA - Instituto Nacional de Matem\u00e1tica Pura e Aplicada (Estrada Dona Castorina 110 Rio de Janeiro 22460-320 - Brazil)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMPA, Estrada Dona Castorina 110, Rio de Janeiro, Brasil 22460-320 (e-mail:","institution_ids":["https://openalex.org/I141883831"]},{"raw_affiliation_string":"IMPA - Instituto Nacional de Matem\u00e1tica Pura e Aplicada (Estrada Dona Castorina 110 Rio de Janeiro 22460-320 - Brazil)","institution_ids":["https://openalex.org/I141883831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108518802","display_name":"Yahya Ould Hamidoune","orcid":null},"institutions":[{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"YAHYA OULD HAMIDOUNE","raw_affiliation_strings":["IMJ - Institut de Math\u00e9matiques de Jussieu (2, place Jussieu 75251 Paris Cedex 05 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMJ - Institut de Math\u00e9matiques de Jussieu (2, place Jussieu 75251 Paris Cedex 05 - France)","institution_ids":["https://openalex.org/I3017942884"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9721,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.77893706,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"4","first_page":"582","last_page":"596"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9988999962806702,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9988999962806702,"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":0.9969000220298767,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/coset","display_name":"Coset","score":0.8815468549728394},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.7534439563751221},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7071948051452637},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.679053783416748},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5062834024429321},{"id":"https://openalex.org/keywords/elementary-proof","display_name":"Elementary proof","score":0.4467162787914276},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.441432923078537},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4147590398788452},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1755582094192505}],"concepts":[{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.8815468549728394},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.7534439563751221},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7071948051452637},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.679053783416748},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5062834024429321},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.4467162787914276},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.441432923078537},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4147590398788452},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1755582094192505},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0963548312000168","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548312000168","pdf_url":null,"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:1110.1961","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1110.1961","pdf_url":"https://arxiv.org/pdf/1110.1961","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-00630441v2","is_oa":true,"landing_page_url":"https://hal.sorbonne-universite.fr/hal-00630441","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics, Probability and Computing, 2012, 21 (4), pp.582-596. &#x27E8;10.1017/S0963548312000168&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1110.1961","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1110.1961","pdf_url":"https://arxiv.org/pdf/1110.1961","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W578591961","https://openalex.org/W842301775","https://openalex.org/W1168421410","https://openalex.org/W1918795846","https://openalex.org/W1966028935","https://openalex.org/W1979212654","https://openalex.org/W1995047211","https://openalex.org/W2003235347","https://openalex.org/W2003616551","https://openalex.org/W2027626405","https://openalex.org/W2045081006","https://openalex.org/W2051793589","https://openalex.org/W2053505259","https://openalex.org/W2100908343","https://openalex.org/W2120758432","https://openalex.org/W2121001629","https://openalex.org/W2141305408","https://openalex.org/W2169775549","https://openalex.org/W2319414173","https://openalex.org/W2495618919","https://openalex.org/W2911280162","https://openalex.org/W2912209775","https://openalex.org/W2949999049","https://openalex.org/W6724150644","https://openalex.org/W6930021426"],"related_works":["https://openalex.org/W2388953866","https://openalex.org/W2349918401","https://openalex.org/W1963889177","https://openalex.org/W2362355910","https://openalex.org/W2126856880","https://openalex.org/W4225242725","https://openalex.org/W1956868877","https://openalex.org/W2140644584","https://openalex.org/W4249910233","https://openalex.org/W3212966857"],"abstract_inverted_index":{"Given":[0],"a":[1,66,109],"finite":[2,79],"subset":[3],"A":[4,17,26,37,41,50,59,64,81,89,93,102],"of":[5,18,21,25,68,72,111,120,123],"an":[6,69,117],"abelian":[7],"group":[8],"G":[9,73,83],",":[10],"we":[11,31,76],"study":[12],"the":[13,124],"set":[14],"k":[15,22,35,45,55,87,97],"\u2227":[16,36,88],"all":[19,44],"sums":[20],"distinct":[23],"elements":[24],".":[27,48,74,100],"In":[28],"this":[29],"paper,":[30],"prove":[32],"that":[33],"|":[34,38,40,42,51,58,60,86,90,92,94,103],"\u2265":[39],"for":[43,84,95],"\u2208":[46,56,98],"{2,.":[47,99],".,|":[49,101],"\u2212":[52,61,104],"2},":[53],"unless":[54],"{2,":[57],"2}":[62],"and":[63],"is":[65],"coset":[67],"elementary":[70,118],"2-subgroup":[71],"Furthermore,":[75],"characterize":[77],"those":[78],"sets":[80],"\u2286":[82],"which":[85],"=":[91],"some":[96],"2}.":[105],"This":[106],"result":[107],"answers":[108],"question":[110],"Diderrich.":[112],"Our":[113],"proof":[114],"relies":[115],"on":[116],"property":[119],"proper":[121],"edge-colourings":[122],"complete":[125],"graph.":[126]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2016-06-24T00:00:00"}