{"id":"https://openalex.org/W4386000397","doi":"https://doi.org/10.1142/s0218196723500595","title":"Directed Ramsey and anti-Ramsey schemes and the Flexible Atom Conjecture","display_name":"Directed Ramsey and anti-Ramsey schemes and the Flexible Atom Conjecture","publication_year":2023,"publication_date":"2023-08-19","ids":{"openalex":"https://openalex.org/W4386000397","doi":"https://doi.org/10.1142/s0218196723500595"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196723500595","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218196723500595","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057539761","display_name":"Jeremy F. Alm","orcid":"https://orcid.org/0000-0002-5300-2101"},"institutions":[{"id":"https://openalex.org/I177898655","display_name":"Lamar University","ror":"https://ror.org/008ms5s18","country_code":"US","type":"education","lineage":["https://openalex.org/I177898655"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jeremy F. Alm","raw_affiliation_strings":["Department of Mathematics, Lamar University, Beaumont, TX 77710, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Lamar University, Beaumont, TX 77710, USA","institution_ids":["https://openalex.org/I177898655"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061484797","display_name":"Michael Levet","orcid":"https://orcid.org/0009-0009-1992-3175"},"institutions":[{"id":"https://openalex.org/I204593131","display_name":"College of Charleston","ror":"https://ror.org/00390t168","country_code":"US","type":"education","lineage":["https://openalex.org/I204593131"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael Levet","raw_affiliation_strings":["Department of Computer Science, College of Charleston, Charleston, SC 29492, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, College of Charleston, Charleston, SC 29492, USA","institution_ids":["https://openalex.org/I204593131"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061484797"],"corresponding_institution_ids":["https://openalex.org/I204593131"],"apc_list":null,"apc_paid":null,"fwci":2.0596,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.85666555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"33","issue":"08","first_page":"1571","last_page":"1598"},"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":0.9984999895095825,"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":0.9984999895095825,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.9980000257492065,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9977999925613403,"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/mathematics","display_name":"Mathematics","score":0.7369452714920044},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.5965368747711182},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.533894419670105},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.5174777507781982},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.509299635887146},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4885903298854828},{"id":"https://openalex.org/keywords/antisymmetric-relation","display_name":"Antisymmetric relation","score":0.41601425409317017},{"id":"https://openalex.org/keywords/ramseys-theorem","display_name":"Ramsey's theorem","score":0.411079466342926},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38846826553344727}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7369452714920044},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5965368747711182},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.533894419670105},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5174777507781982},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.509299635887146},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4885903298854828},{"id":"https://openalex.org/C152401794","wikidata":"https://www.wikidata.org/wiki/Q583760","display_name":"Antisymmetric relation","level":2,"score":0.41601425409317017},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.411079466342926},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38846826553344727},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218196723500595","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1142/s0218196723500595","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4300000071525574}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1168373258","https://openalex.org/W2008963183","https://openalex.org/W2035863510","https://openalex.org/W2068065020","https://openalex.org/W2076685803","https://openalex.org/W2076862903","https://openalex.org/W2078942537","https://openalex.org/W2138079138","https://openalex.org/W2512318899","https://openalex.org/W2946417480","https://openalex.org/W2963467644","https://openalex.org/W3201966940","https://openalex.org/W4210242375","https://openalex.org/W4233185505","https://openalex.org/W4244108936"],"related_works":["https://openalex.org/W1968494762","https://openalex.org/W2527696949","https://openalex.org/W2075821346","https://openalex.org/W2385749544","https://openalex.org/W2046907195","https://openalex.org/W2095817824","https://openalex.org/W2963272825","https://openalex.org/W2036810061","https://openalex.org/W3013762056","https://openalex.org/W4287823680"],"abstract_inverted_index":{"In":[0],"this":[1,72],"paper,":[2,55],"we":[3,128,182],"shed":[4],"new":[5],"light":[6],"on":[7],"the":[8,75,87,184,189],"Flexible":[9],"Atom":[10],"Conjecture.":[11],"We":[12,70,118],"first":[13],"give":[14],"finite":[15,102],"representation":[16,133,145,158],"results":[17],"for":[18],"relation":[19,79],"algebras":[20,98],"[Formula:":[21,24,27,30,33,36,39,42,45,49,57,61,135,147,160],"see":[22,25,28,31,34,37,40,43,46,50,58,62,136,148,161],"text],":[23,26,29,32,35,38,41,44],"text]":[47,59,63,137,149,162],"and":[48,60,91,155],"text].":[51],"Prior":[52],"to":[53,66,86],"our":[54,120],"only":[56],"were":[64],"known":[65],"be":[67,114],"finitely":[68],"representable.":[69],"accomplish":[71],"by":[73,82,188],"generalizing":[74],"notion":[76,107],"of":[77,96,108,115,134,146,159,173],"a":[78,83,101,109],"algebra":[80],"generated":[81],"Ramsey":[84],"scheme":[85,112],"directed":[88,103,110],"(antisymmetric)":[89],"setting,":[90],"then":[92],"showing":[93],"that":[94,130,181],"each":[95],"these":[97],"embeds":[99],"into":[100],"anti-Ramsey":[104,111],"scheme.":[105],"The":[106],"may":[113],"independent":[116],"interest.":[117],"complement":[119],"upper":[121],"bounds":[122],"with":[123],"some":[124],"lower":[125],"bounds.":[126],"Namely,":[127],"show":[129],"any":[131,143,156],"square":[132,144,157],"requires":[138,150,163],"at":[139,151,164],"least":[140,152,165],"14":[141],"points,":[142,154],"11":[153],"12":[166],"points.":[167],"Our":[168],"technique":[169],"adapts":[170],"previous":[171],"work":[172],"Alm":[174],"et":[175],"al.":[176],"[Algebra":[177],"Univ.":[178],"(2022)],":[179],"in":[180],"examine":[183],"combinatorial":[185],"structure":[186],"induced":[187],"flexible":[190],"atom.":[191]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}