{"id":"https://openalex.org/W231079246","doi":"https://doi.org/10.37236/5107","title":"Infinite Gammoids: Minors and Duality","display_name":"Infinite Gammoids: Minors and Duality","publication_year":2015,"publication_date":"2015-12-11","ids":{"openalex":"https://openalex.org/W231079246","doi":"https://doi.org/10.37236/5107","mag":"231079246"},"language":"en","primary_location":{"id":"doi:10.37236/5107","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5107","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p37/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/v22i4p37/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023982920","display_name":"Seyed Hadi Afzali Borujeni","orcid":null},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Seyed Hadi Afzali Borujeni","raw_affiliation_strings":["Universit\u00e4t Hamburg"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Hamburg","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5087261383","display_name":"Hiu Fai Law","orcid":null},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hiu-Fai Law","raw_affiliation_strings":["Universit\u00e4t Hamburg"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Hamburg","institution_ids":["https://openalex.org/I159176309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085436289","display_name":"Malte M\u00fcller","orcid":"https://orcid.org/0000-0003-2871-8359"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Malte M\u00fcller","raw_affiliation_strings":["Universit\u00e4t Hamburg"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t Hamburg","institution_ids":["https://openalex.org/I159176309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5023982920"],"corresponding_institution_ids":["https://openalex.org/I159176309"],"apc_list":null,"apc_paid":null,"fwci":0.95150655,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.75122623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"22","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9884999990463257,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9884999990463257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.8716580867767334},{"id":"https://openalex.org/keywords/dual-polyhedron","display_name":"Dual polyhedron","score":0.7470398545265198},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7224713563919067},{"id":"https://openalex.org/keywords/finitary","display_name":"Finitary","score":0.5759530067443848},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5692070722579956},{"id":"https://openalex.org/keywords/duality","display_name":"Duality (order theory)","score":0.5453800559043884},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.5087314248085022},{"id":"https://openalex.org/keywords/transversal","display_name":"Transversal (combinatorics)","score":0.4484350085258484},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4262066185474396},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4209989309310913},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11843106150627136}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.8716580867767334},{"id":"https://openalex.org/C105313907","wikidata":"https://www.wikidata.org/wiki/Q1053857","display_name":"Dual polyhedron","level":2,"score":0.7470398545265198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7224713563919067},{"id":"https://openalex.org/C2778003309","wikidata":"https://www.wikidata.org/wiki/Q5450381","display_name":"Finitary","level":2,"score":0.5759530067443848},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5692070722579956},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.5453800559043884},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.5087314248085022},{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.4484350085258484},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4262066185474396},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4209989309310913},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11843106150627136},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.37236/5107","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5107","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p37/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:1411.2277","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1411.2277","pdf_url":"https://arxiv.org/pdf/1411.2277","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:231079246","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1411.2277","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:10.1.1.728.9701","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.728.9701","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/ojs/index.php/eljc/article/viewFile/v22i4p37/pdf/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.762.6180","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.762.6180","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/1411.2277.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1411.2277","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1411.2277","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:10.37236/5107","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5107","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i4p37/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":[],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320904","display_name":"Croucher Foundation","ror":"https://ror.org/04741mc34"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W231079246.pdf","grobid_xml":"https://content.openalex.org/works/W231079246.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W774419396","https://openalex.org/W1243305749","https://openalex.org/W1758887450","https://openalex.org/W2029446038","https://openalex.org/W2032319666","https://openalex.org/W2040160028","https://openalex.org/W2058264792","https://openalex.org/W2059161146","https://openalex.org/W2063592986","https://openalex.org/W2084315240","https://openalex.org/W2084562801","https://openalex.org/W2087138194","https://openalex.org/W2950280062","https://openalex.org/W6603834465"],"related_works":["https://openalex.org/W2962901783","https://openalex.org/W1243305749","https://openalex.org/W1176610234","https://openalex.org/W2952597554","https://openalex.org/W2284209083","https://openalex.org/W1758887450","https://openalex.org/W1474861480","https://openalex.org/W3046868629","https://openalex.org/W2951444536","https://openalex.org/W2025974382","https://openalex.org/W2033812757","https://openalex.org/W2095936751","https://openalex.org/W2006277237","https://openalex.org/W2170812129","https://openalex.org/W3197524546","https://openalex.org/W2089493193","https://openalex.org/W3085974363","https://openalex.org/W2744085194","https://openalex.org/W2062599373","https://openalex.org/W2550106438"],"abstract_inverted_index":{"This":[0],"sequel":[1],"to":[2,57,114,151],"Afzali":[3,103],"Borujeni":[4,104],"et.":[5,105],"al.":[6,106],"(2015)":[7],"considers":[8],"minors":[9,43],"and":[10],"duals":[11,122],"of":[12,20,30,44,52,80,91,123,132],"infinite":[13],"gammoids.":[14,47,64],"We":[15],"prove":[16,40],"that":[17,41,68,77,147],"the":[18,49,62,78,121],"class":[19,90,127],"gammoids":[21,45,51,70,93,137],"defined":[22,94],"by":[23,95],"digraphs":[24,96],"not":[25,97,112,149],"containing":[26,98],"a":[27,74,86,129,144],"certain":[28],"type":[29],"substructure,":[31],"called":[32],"an":[33],"outgoing":[34],"comb,":[35],"is":[36,67,73,85,148],"minor-closed.":[37],"Also,":[38],"we":[39,119,142],"finite-rank":[42],"are":[46,55,71,111,138],"Furthermore,":[48],"topological":[50,69],"Carmesin":[53],"(2014)":[54],"proved":[56],"coincide,":[58],"as":[59,128],"matroids,":[60],"with":[61],"finitary":[63],"A":[65],"corollary":[66],"minor-closed.It":[72],"well-known":[75],"fact":[76],"dual":[79,113,150],"any":[81,115,152],"finite":[82,136],"strict":[83,92,145],"gammoid":[84,146],"transversal":[87,116,133],"matroid.":[88,117],"The":[89],"alternating":[99],"combs,":[100],"introduced":[101],"in":[102,125],"(2015),":[107],"contains":[108],"examples":[109],"which":[110],"However,":[118],"describe":[120],"matroids":[124],"this":[126],"natural":[130],"extension":[131],"matroids.":[134],"While":[135],"closed":[139],"under":[140],"duality,":[141],"construct":[143],"gammoid.":[153]},"counts_by_year":[{"year":2015,"cited_by_count":2}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
