{"id":"https://openalex.org/W7214110524","doi":"https://doi.org/10.48550/arxiv.2609.26546","title":"Simple symmetric Venn diagrams with 17, 19 and 23 curves","display_name":"Simple symmetric Venn diagrams with 17, 19 and 23 curves","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214110524","doi":"https://doi.org/10.48550/arxiv.2609.26546"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.26546","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26546","pdf_url":"https://arxiv.org/pdf/2609.26546","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.26546","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5152471598","display_name":"Chris Dzoba","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dzoba, Chris","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5152471598"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9014000296592712,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9014000296592712,"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/T12504","display_name":"Mathematics and Applications","score":0.01730000041425228,"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":0.014100000262260437,"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/jordan-curves","display_name":"Jordan curves","score":0.7699999809265137},{"id":"https://openalex.org/keywords/lean-4-formal-verification","display_name":"Lean 4 formal verification","score":0.7670000195503235}],"concepts":[{"id":"https://openalex.org/C55508974","wikidata":"https://www.wikidata.org/wiki/Q190763","display_name":"Venn diagram","level":2,"score":0.9473000168800354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7057999968528748},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6280999779701233},{"id":"https://openalex.org/C186399060","wikidata":"https://www.wikidata.org/wiki/Q959962","display_name":"Diagram","level":2,"score":0.5879999995231628},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4221999943256378},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.36230000853538513},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3422999978065491},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.31310001015663147},{"id":"https://openalex.org/C70251129","wikidata":"https://www.wikidata.org/wiki/Q260928","display_name":"Jordan curve theorem","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27720001339912415}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.26546","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26546","pdf_url":"https://arxiv.org/pdf/2609.26546","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.26546","doi":"https://doi.org/10.48550/arxiv.2609.26546","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.26546","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.26546","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.26546","pdf_url":"https://arxiv.org/pdf/2609.26546","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214110524.pdf","grobid_xml":"https://content.openalex.org/works/W7214110524.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W1821514708"],"related_works":["https://openalex.org/W2008612935","https://openalex.org/W194770738","https://openalex.org/W2599617186","https://openalex.org/W1999899863","https://openalex.org/W2151936745","https://openalex.org/W2601363349","https://openalex.org/W23821587","https://openalex.org/W2135799994","https://openalex.org/W1544981408","https://openalex.org/W7096663562"],"abstract_inverted_index":{"We":[0],"exhibit":[1],"simple,":[2,43],"rotationally":[3],"symmetric":[4],"Venn":[5,51],"diagrams":[6,41,52,67,94,184,199],"with":[7,10,14,28,119],"17":[8],"curves,":[9],"19":[11],"curves":[12,19,59,70,82,126],"and":[13,36,62,84,91,168,197],"23":[15,125],"curves:":[16],"$n$":[17],"Jordan":[18],"carried":[20],"to":[21,80],"one":[22,30,161],"another":[23],"by":[24,97,134,157,174],"rotation":[25],"through":[26,71],"$2\u03c0/n$,":[27],"every":[29,44,55],"of":[31,58,104,164,182],"the":[32,40,105,116,127,138,140,146,165,183,190,195],"$2^n$":[33],"regions":[34,109,136],"present":[35],"connected":[37],"and,":[38],"since":[39],"are":[42,185],"crossing":[45],"on":[46,101],"exactly":[47],"two":[48,132,141],"curves.":[49],"Symmetric":[50],"exist":[53],"for":[54,131],"prime":[56],"number":[57],"(Griggs,":[60],"Killian":[61],"Savage,":[63],"2004),":[64],"but":[65],"those":[66],"have":[68,202],"many":[69],"a":[72,98,158,175],"point;":[73],"simple":[74],"ones":[75],"were":[76,95,145],"known":[77],"only":[78],"up":[79],"13":[81],"(Mamakani":[83],"Ruskey,":[85],"2014).":[86],"Four":[87],"17-curve,":[88],"twelve":[89],"19-curve":[90],"six":[92],"23-curve":[93,169],"found":[96,194,203],"Metropolis":[99],"walk":[100,128],"rotation-invariant":[102],"quadrangulations":[103],"sphere":[106],"in":[107,178],"which":[108,187],"may":[110],"temporarily":[111],"be":[112],"duplicated,":[113],"started":[114],"from":[115],"Griggs-Killian-Savage":[117],"diagram":[118,154],"its":[120],"multiple":[121],"crossings":[122],"resolved.":[123],"At":[124],"was":[129],"held":[130],"weeks":[133],"duplicated":[135],"near":[137],"poles;":[139],"lineages":[142],"that":[143,193],"finished":[144],"first":[147],"whose":[148],"$E=92$":[149],"states":[150],"had":[151],"none.":[152],"Every":[153],"is":[155,188],"given":[156],"machine-checkable":[159],"certificate;":[160],"certificate":[162],"each":[163],"17-,":[166],"19-":[167],"sizes":[170],"has":[171],"been":[172],"verified":[173],"formal":[176],"proof":[177],"Lean":[179],"4.":[180],"All":[181],"non-monotone,":[186],"why":[189],"crossing-sequence":[191],"searches":[192],"11-":[196],"13-curve":[198],"could":[200],"not":[201],"them.":[204]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-24T00:00:00"}
