{"id":"https://openalex.org/W2038010519","doi":"https://doi.org/10.1016/0097-3165(72)90089-1","title":"Lower bounds for certain types of van der Waerden numbers","display_name":"Lower bounds for certain types of van der Waerden numbers","publication_year":1972,"publication_date":"1972-01-01","ids":{"openalex":"https://openalex.org/W2038010519","doi":"https://doi.org/10.1016/0097-3165(72)90089-1","mag":"2038010519"},"language":"en","primary_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/0097-3165(72)90089-1","pdf_url":null,"source":{"id":"https://openalex.org/S128556326","display_name":"Journal of Combinatorial Theory Series A","issn_l":"0097-3165","issn":["0097-3165","1096-0899"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"publishedVersion","is_accepted":true,"is_published":true},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://doi.org/10.1016/0097-3165(72)90089-1","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085899996","display_name":"H. L. Abbott","orcid":null},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"H. L. Abbott","raw_affiliation_strings":["University of Alberta, Edmonton, and University of Saskatchewan, Regina, Canada"],"affiliations":[{"raw_affiliation_string":"University of Alberta, Edmonton, and University of Saskatchewan, Regina, Canada","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108435597","display_name":"Denis Hanson","orcid":null},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Denis Hanson","raw_affiliation_strings":["University of Alberta, Edmonton, and University of Saskatchewan, Regina, Canada"],"affiliations":[{"raw_affiliation_string":"University of Alberta, Edmonton, and University of Saskatchewan, Regina, Canada","institution_ids":["https://openalex.org/I154425047"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3320,"currency":"USD","value_usd":3320,"provenance":"doaj"},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":8,"citation_normalized_percentile":{"value":0.578498,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":80,"max":81},"biblio":{"volume":"12","issue":"1","first_page":"143","last_page":"146"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9969,"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":0.9969,"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/T11166","display_name":"Prime Number Theory and L-Functions","score":0.9949,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11567","display_name":"Automata Theory and Formal Languages","score":0.9927,"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/arithmetic-progressions","display_name":"Arithmetic Progressions","score":0.498435}],"concepts":[{"id":"https://openalex.org/C116493835","wikidata":"https://www.wikidata.org/wiki/Q764287","display_name":"Van der Waerden's theorem","level":2,"score":0.9842899},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5345183},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.51744324}],"mesh":[],"locations_count":1,"locations":[{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/0097-3165(72)90089-1","pdf_url":null,"source":{"id":"https://openalex.org/S128556326","display_name":"Journal of Combinatorial Theory Series A","issn_l":"0097-3165","issn":["0097-3165","1096-0899"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"publishedVersion","is_accepted":true,"is_published":true}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://doi.org/10.1016/0097-3165(72)90089-1","pdf_url":null,"source":{"id":"https://openalex.org/S128556326","display_name":"Journal of Combinatorial Theory Series A","issn_l":"0097-3165","issn":["0097-3165","1096-0899"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"publisher-specific-oa","license_id":"https://openalex.org/licenses/publisher-specific-oa","version":"publishedVersion","is_accepted":true,"is_published":true},"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":3,"referenced_works":["https://openalex.org/W1499542263","https://openalex.org/W2067189483","https://openalex.org/W625472031"],"related_works":["https://openalex.org/W2953008743","https://openalex.org/W2890157477","https://openalex.org/W2580503325","https://openalex.org/W2391021702","https://openalex.org/W2376783244","https://openalex.org/W2077043254","https://openalex.org/W2033895221","https://openalex.org/W2025456998","https://openalex.org/W1987972399","https://openalex.org/W1496540776"],"abstract_inverted_index":{"Denote":[0],"by":[1],"B":[2,19,62],"(":[3,20,63],"k":[4,21,33,64],",":[5,22,65],"l":[6,23,46,66],")":[7,24],"the":[8,14,39,52],"least":[9,36],"integer":[10],"such":[11],"that,":[12],"if":[13],"numbers":[15],"1,":[16],"2,":[17],"3,\u2026,":[18],"+":[25,47],"1":[26,48],"are":[27,59],"partitioned":[28],"in":[29],"any":[30],"way":[31],"into":[32],"sets,":[34],"at":[35],"one":[37],"of":[38,45],"sets":[40],"contains":[41],"an":[42],"arithmetic":[43],"progression":[44],"terms,":[49],"together":[50],"with":[51],"common":[53],"difference.":[54],"Some":[55],"new":[56],"lower":[57],"bounds":[58],"derived":[60],"for":[61],").":[67]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2038010519","counts_by_year":[],"updated_date":"2024-10-21T11:33:32.890789","created_date":"2016-06-24"}