{"id":"https://openalex.org/W1880047185","doi":"https://doi.org/10.37236/4356","title":"An Abstraction of Whitney's Broken Circuit Theorem","display_name":"An Abstraction of Whitney's Broken Circuit Theorem","publication_year":2014,"publication_date":"2014-11-13","ids":{"openalex":"https://openalex.org/W1880047185","doi":"https://doi.org/10.37236/4356","mag":"1880047185"},"language":"en","primary_location":{"id":"doi:10.37236/4356","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4356","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p32/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/v21i4p32/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064473834","display_name":"Klaus Dohmen","orcid":"https://orcid.org/0000-0002-8076-4101"},"institutions":[{"id":"https://openalex.org/I116397343","display_name":"Hochschule Mittweida","ror":"https://ror.org/024ga3r86","country_code":"DE","type":"education","lineage":["https://openalex.org/I116397343"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Klaus Dohmen","raw_affiliation_strings":["Hochschule Mittweida\r\nUniversity of Applied Sciences\r\nDept. of Mathematics\r\n09648 Mittweida","Hochschule Mittweida#R##N#University of Applied Sciences#R##N#Dept. of Mathematics#R##N#09648 Mittweida"],"affiliations":[{"raw_affiliation_string":"Hochschule Mittweida\r\nUniversity of Applied Sciences\r\nDept. of Mathematics\r\n09648 Mittweida","institution_ids":["https://openalex.org/I116397343"]},{"raw_affiliation_string":"Hochschule Mittweida#R##N#University of Applied Sciences#R##N#Dept. of Mathematics#R##N#09648 Mittweida","institution_ids":["https://openalex.org/I116397343"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039051003","display_name":"Martin Trinks","orcid":"https://orcid.org/0000-0002-5613-2032"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Martin Trinks","raw_affiliation_strings":["Center for Combinatorics\r\nNankai University\r\nTianjin 300071","Center for Combinatorics#R##N#Nankai University#R##N#Tianjin 300071"],"affiliations":[{"raw_affiliation_string":"Center for Combinatorics\r\nNankai University\r\nTianjin 300071","institution_ids":["https://openalex.org/I205237279"]},{"raw_affiliation_string":"Center for Combinatorics#R##N#Nankai University#R##N#Tianjin 300071","institution_ids":["https://openalex.org/I205237279"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064473834"],"corresponding_institution_ids":["https://openalex.org/I116397343"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.0523531,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"21","issue":"4","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":0.9997000098228455,"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":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9990000128746033,"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":0.8009519577026367},{"id":"https://openalex.org/keywords/chromatic-polynomial","display_name":"Chromatic polynomial","score":0.6907764673233032},{"id":"https://openalex.org/keywords/tutte-polynomial","display_name":"Tutte polynomial","score":0.614176869392395},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5495142936706543},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5377379655838013},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2783610224723816},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.15981271862983704},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.12806639075279236}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8009519577026367},{"id":"https://openalex.org/C126385604","wikidata":"https://www.wikidata.org/wiki/Q1087609","display_name":"Chromatic polynomial","level":3,"score":0.6907764673233032},{"id":"https://openalex.org/C14447369","wikidata":"https://www.wikidata.org/wiki/Q7857002","display_name":"Tutte polynomial","level":5,"score":0.614176869392395},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5495142936706543},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5377379655838013},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2783610224723816},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.15981271862983704},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.12806639075279236}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/4356","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4356","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p32/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:1404.5480","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.5480","pdf_url":"https://arxiv.org/pdf/1404.5480","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":"","raw_type":"text"},{"id":"mag:1880047185","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1404.5480v3","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":"pmh:oai:CiteSeerX.psu:10.1.1.752.5450","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.752.5450","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1404.5480.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1404.5480","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1404.5480","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:10.37236/4356","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4356","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v21i4p32/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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.8199999928474426}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1880047185.pdf","grobid_xml":"https://content.openalex.org/works/W1880047185.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W19887065","https://openalex.org/W219446931","https://openalex.org/W757380603","https://openalex.org/W1495550473","https://openalex.org/W1515550648","https://openalex.org/W1987473018","https://openalex.org/W1993865305","https://openalex.org/W2001708643","https://openalex.org/W2027446053","https://openalex.org/W2029317359","https://openalex.org/W2040661328","https://openalex.org/W2045967420","https://openalex.org/W2061575883","https://openalex.org/W2065094840","https://openalex.org/W2092653160","https://openalex.org/W2095407242","https://openalex.org/W2126209209","https://openalex.org/W2152710849","https://openalex.org/W2313098266","https://openalex.org/W2319873605","https://openalex.org/W2592808828","https://openalex.org/W2798588639","https://openalex.org/W3037290570","https://openalex.org/W6647015059","https://openalex.org/W6666016217"],"related_works":["https://openalex.org/W2963090365","https://openalex.org/W2767886788","https://openalex.org/W1541384556","https://openalex.org/W2125630006","https://openalex.org/W1598581344","https://openalex.org/W2950175719","https://openalex.org/W1976991503","https://openalex.org/W3101233038","https://openalex.org/W2180586453","https://openalex.org/W2081027509","https://openalex.org/W2037454942","https://openalex.org/W3101380633","https://openalex.org/W1998101090","https://openalex.org/W2975446003","https://openalex.org/W3203379035","https://openalex.org/W1542290583","https://openalex.org/W2963570298","https://openalex.org/W2017399891","https://openalex.org/W1994747108","https://openalex.org/W1547955525"],"abstract_inverted_index":{"We":[0,45,167],"establish":[1,169],"a":[2,15,27,33,58,64,74,90,104,113,125],"broad":[3],"generalization":[4,106,173],"of":[5,14,19,39,57,63,73,79,98,107,112,124,149,174,182],"Whitney's":[6,175],"broken":[7,176],"circuit":[8,177],"theorem":[9,114,178],"on":[10,120],"the":[11,36,49,53,60,66,77,108,121,134,147,150,159,180],"chromatic":[12,61],"polynomial":[13,51,56,62,68],"graph":[16],"to":[17,48,116],"sums":[18],"type":[20],"$\\sum_{A\\subseteq":[21],"S}":[22],"f(A)$":[23],"where":[24],"$S$":[25,40],"is":[26,32],"finite":[28,126],"set":[29,38],"and":[30,52,69,76,86,92,111,118,142,146],"$f$":[31],"mapping":[34],"from":[35],"power":[37],"into":[41],"an":[42,170],"abelian":[43],"group.":[44],"give":[46],"applications":[47,97],"domination":[50],"subgraph":[54],"component":[55],"graph,":[59],"hypergraph,":[65],"characteristic":[67],"Crapo's":[70],"beta":[71],"invariant":[72],"matroid,":[75],"principle":[78],"inclusion-exclusion.":[80],"Thus,":[81],"we":[82,102,154],"discover":[83],"several":[84],"known":[85],"new":[87,105,156],"results":[88],"in":[89,179],"concise":[91],"unified":[93],"way.":[94],"As":[95],"further":[96],"our":[99],"main":[100],"result,":[101],"derive":[103],"maximums-minimums":[109],"identity":[110],"due":[115],"Blass":[117],"Sagan":[119],"M\u00f6bius":[122,136],"function":[123,141,153],"lattice,":[127],"which":[128],"generalizes":[129],"Rota's":[130],"crosscut":[131],"theorem.":[132],"For":[133],"classical":[135],"function,":[137],"both":[138],"Euler's":[139],"totient":[140],"its":[143],"Dirichlet":[144],"inverse,":[145],"reciprocal":[148],"Riemann":[151],"zeta":[152],"obtain":[155],"expansions":[157],"involving":[158],"greatest":[160],"common":[161,165],"divisor":[162],"resp.":[163],"least":[164],"multiple.":[166],"finally":[168],"even":[171],"broader":[172],"context":[181],"convex":[183],"geometries":[184],"(antimatroids).":[185]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}