{"id":"https://openalex.org/W3132915420","doi":"https://doi.org/10.37236/10249","title":"Integer Colorings with No Rainbow 3-Term Arithmetic Progression","display_name":"Integer Colorings with No Rainbow 3-Term Arithmetic Progression","publication_year":2022,"publication_date":"2022-05-06","ids":{"openalex":"https://openalex.org/W3132915420","doi":"https://doi.org/10.37236/10249","mag":"3132915420"},"language":"en","primary_location":{"id":"doi:10.37236/10249","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10249","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i2p28/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":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i2p28/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101784961","display_name":"Xihe Li","orcid":"https://orcid.org/0000-0002-7070-1174"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]},{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["CN","NL"],"is_corresponding":false,"raw_author_name":"Xihe Li","raw_affiliation_strings":["Faculty of Electrical Engineering, Mathematics and Computer Science University of Twente P.O. Box 217, 7500 AE Enschede, The Netherlands","School of Mathematics and Statistics Northwestern Polytechnical University Xi'an, Shaanxi 710129, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering, Mathematics and Computer Science University of Twente P.O. Box 217, 7500 AE Enschede, The Netherlands","institution_ids":["https://openalex.org/I94624287"]},{"raw_affiliation_string":"School of Mathematics and Statistics Northwestern Polytechnical University Xi'an, Shaanxi 710129, PR China","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068613759","display_name":"Hajo Broersma","orcid":"https://orcid.org/0000-0002-4678-3210"},"institutions":[{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Hajo Broersma","raw_affiliation_strings":["University of Twente"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Twente","institution_ids":["https://openalex.org/I94624287"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064861169","display_name":"Ligong Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]},{"id":"https://openalex.org/I94624287","display_name":"University of Twente","ror":"https://ror.org/006hf6230","country_code":"NL","type":"education","lineage":["https://openalex.org/I94624287"]}],"countries":["CN","NL"],"is_corresponding":false,"raw_author_name":"Ligong Wang","raw_affiliation_strings":["Faculty of Electrical Engineering, Mathematics and Computer Science University of Twente P.O. Box 217, 7500 AE Enschede, The Netherlands","School of Mathematics and Statistics Northwestern Polytechnical University Xi'an, Shaanxi 710129, PR China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Electrical Engineering, Mathematics and Computer Science University of Twente P.O. Box 217, 7500 AE Enschede, The Netherlands","institution_ids":["https://openalex.org/I94624287"]},{"raw_affiliation_string":"School of Mathematics and Statistics Northwestern Polytechnical University Xi'an, Shaanxi 710129, PR China","institution_ids":["https://openalex.org/I17145004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7849,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.88368844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"29","issue":"2","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":0.9998999834060669,"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":0.9998999834060669,"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":0.9850999712944031,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9796000123023987,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rainbow","display_name":"Rainbow","score":0.9467017650604248},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.767235279083252},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7174269556999207},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7138262987136841},{"id":"https://openalex.org/keywords/arithmetic-progression","display_name":"Arithmetic progression","score":0.695367693901062},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6182371973991394},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.4224252998828888},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4031539559364319},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08888867497444153},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0426957905292511}],"concepts":[{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.9467017650604248},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.767235279083252},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7174269556999207},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7138262987136841},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.695367693901062},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6182371973991394},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.4224252998828888},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4031539559364319},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08888867497444153},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0426957905292511},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/10249","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10249","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i2p28/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:ris.utwente.nl:openaire_cris_publications/c55fbf55-c71c-4a7f-8e10-f69598298aa5","is_oa":false,"landing_page_url":"https://research.utwente.nl/en/publications/c55fbf55-c71c-4a7f-8e10-f69598298aa5","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Li, X, Broersma, H & Wang, L 2022, 'Integer colorings with no rainbow 3-term arithmetic progression', The Electronic journal of combinatorics, vol. 29, no. 2, P2.28. https://doi.org/10.37236/10249","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:2102.08995","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.08995","pdf_url":"https://arxiv.org/pdf/2102.08995","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":"pmh:oai:ris.utwente.nl:publications/c55fbf55-c71c-4a7f-8e10-f69598298aa5","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85129460943&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"doi:10.37236/10249","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10249","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i2p28/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/G1402806183","display_name":null,"funder_award_id":"201906290174","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5445264884","display_name":null,"funder_award_id":"201906290174","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"},{"id":"https://openalex.org/G5926367349","display_name":"\u6709\u5411\u56fe\u4e0e\u7b26\u53f7\u6709\u5411\u56fe\u7684\u8c31\u7406\u8bba\u7814\u7a76","funder_award_id":"11871398","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8495349718","display_name":null,"funder_award_id":"11871398","funder_id":"https://openalex.org/F4320322725","funder_display_name":"China Scholarship Council"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3132915420.pdf","grobid_xml":"https://content.openalex.org/works/W3132915420.grobid-xml"},"referenced_works_count":41,"referenced_works":["https://openalex.org/W8120809","https://openalex.org/W45561327","https://openalex.org/W1484548402","https://openalex.org/W1489006728","https://openalex.org/W1490794915","https://openalex.org/W1502732720","https://openalex.org/W1613991166","https://openalex.org/W1992296250","https://openalex.org/W2009196521","https://openalex.org/W2034838716","https://openalex.org/W2066501202","https://openalex.org/W2342553262","https://openalex.org/W2356880738","https://openalex.org/W2759922368","https://openalex.org/W2765793708","https://openalex.org/W2885443064","https://openalex.org/W2904423657","https://openalex.org/W2905926941","https://openalex.org/W2962762798","https://openalex.org/W2962839324","https://openalex.org/W2962868604","https://openalex.org/W2963410422","https://openalex.org/W2963417541","https://openalex.org/W2963474057","https://openalex.org/W2963611066","https://openalex.org/W2963811178","https://openalex.org/W2994143791","https://openalex.org/W2996732696","https://openalex.org/W2998345723","https://openalex.org/W3032271463","https://openalex.org/W3038100514","https://openalex.org/W3044702813","https://openalex.org/W3101177936","https://openalex.org/W3148148526","https://openalex.org/W4301288248","https://openalex.org/W4301717965","https://openalex.org/W4377818744","https://openalex.org/W6636595062","https://openalex.org/W6659192116","https://openalex.org/W6667614299","https://openalex.org/W6785497190"],"related_works":["https://openalex.org/W2924691597","https://openalex.org/W3194315539","https://openalex.org/W3132915420","https://openalex.org/W4299701612","https://openalex.org/W4297666526","https://openalex.org/W2171984564","https://openalex.org/W2159445144","https://openalex.org/W4297994440","https://openalex.org/W2010459743","https://openalex.org/W1967777504"],"abstract_inverted_index":{"In":[0],"this":[1,37],"paper,":[2],"we":[3,30],"study":[4],"the":[5,17,33,47,62,83],"rainbow":[6,25,51,66],"Erd\u0151s-Rothschild":[7],"problem":[8],"with":[9,36],"respect":[10],"to":[11],"3-term":[12,26,52,67],"arithmetic":[13,27,53,68],"progressions.":[14],"We":[15,41],"obtain":[16],"asymptotic":[18],"number":[19,49,64],"of":[20,22,50,59,65,71,86],"$r$-colorings":[21,55,70],"$[n]$":[23,45],"without":[24],"progressions,":[28],"and":[29,80],"show":[31],"that":[32,44],"typical":[34],"colorings":[35],"property":[38],"are":[39],"2-colorings.":[40],"also":[42],"prove":[43],"attains":[46],"maximum":[48],"progression-free":[54,69],"among":[56],"all":[57],"subsets":[58],"$[n]$.":[60],"Moreover,":[61],"exact":[63],"$\\mathbb{Z}_p$":[72,81],"is":[73,77,82],"obtained,":[74],"where":[75],"$p$":[76],"any":[78],"prime":[79],"cyclic":[84],"group":[85],"order":[87],"$p$.":[88]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}