{"id":"https://openalex.org/W2922085044","doi":"https://doi.org/10.37236/8895","title":"Maximum $k$-Sum $\\mathbf{n}$-Free Sets of the 2-Dimensional Integer Lattice","display_name":"Maximum $k$-Sum $\\mathbf{n}$-Free Sets of the 2-Dimensional Integer Lattice","publication_year":2020,"publication_date":"2020-10-02","ids":{"openalex":"https://openalex.org/W2922085044","doi":"https://doi.org/10.37236/8895","mag":"2922085044"},"language":"en","primary_location":{"id":"doi:10.37236/8895","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8895","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p2/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p2/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025173209","display_name":"Ilkyoo Choi","orcid":"https://orcid.org/0000-0003-1102-7922"},"institutions":[{"id":"https://openalex.org/I83436808","display_name":"Hankuk University of Foreign Studies","ror":"https://ror.org/051q2m369","country_code":"KR","type":"education","lineage":["https://openalex.org/I83436808"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Ilkyoo Choi","raw_affiliation_strings":["Hankuk University of Foreign Studies#TAB#"],"affiliations":[{"raw_affiliation_string":"Hankuk University of Foreign Studies#TAB#","institution_ids":["https://openalex.org/I83436808"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005237525","display_name":"Ringi Kim","orcid":"https://orcid.org/0000-0001-5561-6513"},"institutions":[{"id":"https://openalex.org/I157485424","display_name":"Korea Advanced Institute of Science and Technology","ror":"https://ror.org/05apxxy63","country_code":"KR","type":"education","lineage":["https://openalex.org/I157485424"]},{"id":"https://openalex.org/I4210099236","display_name":"Kootenay Association for Science & Technology","ror":"https://ror.org/011pv9p44","country_code":"CA","type":"nonprofit","lineage":["https://openalex.org/I4210099236"]}],"countries":["CA","KR"],"is_corresponding":false,"raw_author_name":"Ringi Kim","raw_affiliation_strings":["KAIST"],"affiliations":[{"raw_affiliation_string":"KAIST","institution_ids":["https://openalex.org/I4210099236","https://openalex.org/I157485424"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101459574","display_name":"Boram Park","orcid":"https://orcid.org/0000-0003-4102-1206"},"institutions":[{"id":"https://openalex.org/I57664883","display_name":"Ajou University","ror":"https://ror.org/03tzb2h73","country_code":"KR","type":"education","lineage":["https://openalex.org/I57664883"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Boram Park","raw_affiliation_strings":["Ajou University,"],"affiliations":[{"raw_affiliation_string":"Ajou University,","institution_ids":["https://openalex.org/I57664883"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025173209"],"corresponding_institution_ids":["https://openalex.org/I83436808"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.06126847,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"4","first_page":null,"last_page":null},"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":0.9912999868392944,"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":0.9912999868392944,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9801999926567078,"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"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9710999727249146,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/combinatorics","display_name":"Combinatorics","score":0.7949172258377075},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.7696799039840698},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5864951014518738},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.565101146697998},{"id":"https://openalex.org/keywords/integer-lattice","display_name":"Integer lattice","score":0.535212516784668},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5017340183258057},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.40000250935554504},{"id":"https://openalex.org/keywords/half-integer","display_name":"Half-integer","score":0.1719168722629547},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.13995110988616943}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7949172258377075},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.7696799039840698},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5864951014518738},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.565101146697998},{"id":"https://openalex.org/C142885752","wikidata":"https://www.wikidata.org/wiki/Q1252145","display_name":"Integer lattice","level":3,"score":0.535212516784668},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5017340183258057},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40000250935554504},{"id":"https://openalex.org/C56863137","wikidata":"https://www.wikidata.org/wiki/Q743139","display_name":"Half-integer","level":2,"score":0.1719168722629547},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.13995110988616943},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/8895","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8895","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p2/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1903.04132","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1903.04132","pdf_url":"https://arxiv.org/pdf/1903.04132","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":null,"raw_type":"text"},{"id":"mag:2922085044","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1903.04132.pdf","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.1903.04132","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1903.04132","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:10.37236/8895","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8895","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p2/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2820426551","display_name":null,"funder_award_id":"NRF-2018R1D1A1B0704","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G2970261365","display_name":null,"funder_award_id":"NRF-2018R1C1B6003786","funder_id":"https://openalex.org/F4320322030","funder_display_name":"Ministry of Science, ICT and Future Planning"},{"id":"https://openalex.org/G3034753964","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"},{"id":"https://openalex.org/G3086744019","display_name":null,"funder_award_id":"2018R1C1B6003","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G342704958","display_name":null,"funder_award_id":"funded","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G3942910960","display_name":null,"funder_award_id":"(NRF) grant","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G5637693390","display_name":null,"funder_award_id":"NRF-2018R1C1B6003577","funder_id":"https://openalex.org/F4320322030","funder_display_name":"Ministry of Science, ICT and Future Planning"},{"id":"https://openalex.org/G5812840432","display_name":null,"funder_award_id":"NRF-2018R1C1B6003577","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G5830618976","display_name":null,"funder_award_id":"NRF-2018R1D1A1B07043","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G6225209897","display_name":null,"funder_award_id":"2018R1D1A1B0704","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G8011125346","display_name":null,"funder_award_id":"2018R1D1A1B0","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G982292920","display_name":null,"funder_award_id":"NRF-20","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320320279","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86"},{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320321227","display_name":"Hankuk University of Foreign Studies","ror":"https://ror.org/051q2m369"},{"id":"https://openalex.org/F4320322030","display_name":"Ministry of Science, ICT and Future Planning","ror":"https://ror.org/032e49973"},{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"},{"id":"https://openalex.org/F4320328359","display_name":"Ministry of Science and ICT, South Korea","ror":"https://ror.org/01wpjm123"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2922085044.pdf","grobid_xml":"https://content.openalex.org/works/W2922085044.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W45561327","https://openalex.org/W2057739679","https://openalex.org/W2070496958","https://openalex.org/W2117908084","https://openalex.org/W2133724548","https://openalex.org/W2139279621","https://openalex.org/W2500947654","https://openalex.org/W2505456687","https://openalex.org/W2576511410","https://openalex.org/W2760816055","https://openalex.org/W2906147409","https://openalex.org/W2917664358","https://openalex.org/W2962868604","https://openalex.org/W2963876339","https://openalex.org/W2964105244","https://openalex.org/W6633621516","https://openalex.org/W6693210832"],"related_works":["https://openalex.org/W3090336338","https://openalex.org/W1966768475","https://openalex.org/W184408225","https://openalex.org/W2072510267","https://openalex.org/W2155187680","https://openalex.org/W2100983198","https://openalex.org/W2242573402","https://openalex.org/W3009078167","https://openalex.org/W1574691718","https://openalex.org/W2019903106","https://openalex.org/W1980290091","https://openalex.org/W2395867189","https://openalex.org/W2359264276","https://openalex.org/W2467114759","https://openalex.org/W3165718615","https://openalex.org/W2041751740","https://openalex.org/W2963605982","https://openalex.org/W2310381493","https://openalex.org/W2092052244","https://openalex.org/W2301250009"],"abstract_inverted_index":{"For":[0,11,53],"a":[1,12,25,33,54,73],"positive":[2,19,61],"integer":[3,14,56],"$n$,":[4,24,66],"let":[5],"$[n]$":[6],"denote":[7],"$\\{1,":[8],"\\ldots,":[9,46],"n\\}$.":[10],"2-dimensional":[13,55],"lattice":[15,57],"point":[16,58],"$\\mathbf{b}$":[17,59],"and":[18,23,60,65],"integers":[20,62],"$k\\geq":[21,63],"2$":[22,64],"$k$-sum":[26,74],"$\\mathbf{b}$-free":[27,75],"set":[28,76,89],"of":[29,36,72,77,85],"$[n]\\times":[30,37,78],"[n]$":[31,38],"is":[32,81],"subset":[34],"$S$":[35,49],"such":[39],"that":[40],"there":[41],"are":[42],"no":[43],"elements":[44],"$\\mathbf{a}_1,":[45],"\\mathbf{a}_k$":[47],"in":[48,91],"satisfying":[50],"$\\mathbf{a}_1+\\cdots+\\mathbf{a}_k":[51],"=\\mathbf{b}$.":[52],"we":[67],"determine":[68],"the":[69,82,86],"maximum":[70],"density":[71],"[n]$.":[79],"This":[80],"first":[83],"investigation":[84],"non-homogeneous":[87],"sum-free":[88],"problem":[90],"higher":[92],"dimensions.":[93]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
