{"id":"https://openalex.org/W4253943746","doi":"https://doi.org/10.37236/970","title":"On Subsequence Sums of a Zero-sum Free Sequence","display_name":"On Subsequence Sums of a Zero-sum Free Sequence","publication_year":2007,"publication_date":"2007-07-26","ids":{"openalex":"https://openalex.org/W4253943746","doi":"https://doi.org/10.37236/970"},"language":"en","primary_location":{"id":"doi:10.37236/970","is_oa":true,"landing_page_url":"https://doi.org/10.37236/970","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r52/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r52/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110899962","display_name":"Fang Sun","orcid":null},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fang Sun","raw_affiliation_strings":["Center for Combinatorics, LPMC Nankai University, Tianjin, P.R. China"],"affiliations":[{"raw_affiliation_string":"Center for Combinatorics, LPMC Nankai University, Tianjin, P.R. China","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110899962"],"corresponding_institution_ids":["https://openalex.org/I205237279"],"apc_list":null,"apc_paid":null,"fwci":1.4361,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84344508,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"14","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9991000294685364,"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/T11130","display_name":"Coding theory and cryptography","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/subsequence","display_name":"Subsequence","score":0.9704881906509399},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.878307044506073},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8580338954925537},{"id":"https://openalex.org/keywords/longest-increasing-subsequence","display_name":"Longest increasing subsequence","score":0.8283078670501709},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.723820686340332},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.6686766147613525},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.604495108127594},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5719942450523376},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.41263002157211304},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4105522632598877},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.03867533802986145},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0375291109085083}],"concepts":[{"id":"https://openalex.org/C137877099","wikidata":"https://www.wikidata.org/wiki/Q1332977","display_name":"Subsequence","level":3,"score":0.9704881906509399},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.878307044506073},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8580338954925537},{"id":"https://openalex.org/C170006305","wikidata":"https://www.wikidata.org/wiki/Q4183855","display_name":"Longest increasing subsequence","level":4,"score":0.8283078670501709},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.723820686340332},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6686766147613525},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.604495108127594},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5719942450523376},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.41263002157211304},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4105522632598877},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.03867533802986145},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0375291109085083},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","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":2,"locations":[{"id":"doi:10.37236/970","is_oa":true,"landing_page_url":"https://doi.org/10.37236/970","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r52/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.86.6272","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.6272","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_14/PDF/v14i1r52.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/970","is_oa":true,"landing_page_url":"https://doi.org/10.37236/970","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r52/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4699999988079071,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3151526626","display_name":null,"funder_award_id":"PCSIRT","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4253943746.pdf","grobid_xml":"https://content.openalex.org/works/W4253943746.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1168421410","https://openalex.org/W1990678489","https://openalex.org/W2002764339","https://openalex.org/W2070302103","https://openalex.org/W2091770425","https://openalex.org/W4210570486","https://openalex.org/W6828130914"],"related_works":["https://openalex.org/W2969919693","https://openalex.org/W3122601395","https://openalex.org/W2125120904","https://openalex.org/W4225868058","https://openalex.org/W2035123411","https://openalex.org/W2112772040","https://openalex.org/W2131191265","https://openalex.org/W4389489786","https://openalex.org/W1540010783","https://openalex.org/W2031919030"],"abstract_inverted_index":{"Let":[0,20],"$G$":[1,28],"be":[2,13,31],"a":[3,14,37],"finite":[4],"abelian":[5],"group":[6],"with":[7,56,77],"exponent":[8],"$m$,":[9],"and":[10,50,70],"let":[11],"$S$":[12,51],"sequence":[15],"of":[16,25,40],"elements":[17,26],"in":[18,27],"$G$.":[19],"$f(S)$":[21],"denote":[22],"the":[23,34,74,78],"number":[24],"which":[29],"can":[30],"expressed":[32],"as":[33],"sum":[35],"over":[36],"nonempty":[38,54],"subsequence":[39,55],"$S$.":[41],"In":[42],"this":[43],"paper,":[44],"we":[45],"show":[46],"that,":[47],"if":[48],"$|S|=m$":[49],"contains":[52],"no":[53],"zero":[57],"sum,":[58],"then":[59],"$f(S)\\geq":[60],"2m-1$.":[61],"This":[62],"answers":[63],"an":[64],"open":[65],"question":[66],"formulated":[67],"by":[68],"Gao":[69],"Leader.":[71],"They":[72],"proved":[73],"same":[75],"result":[76],"restriction":[79],"$(m,6)=1$.":[80]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
