{"id":"https://openalex.org/W1597200034","doi":"https://doi.org/10.37236/4671","title":"Gammoids, Pseudomodularity and Flatness Degree","display_name":"Gammoids, Pseudomodularity and Flatness Degree","publication_year":2015,"publication_date":"2015-03-06","ids":{"openalex":"https://openalex.org/W1597200034","doi":"https://doi.org/10.37236/4671","mag":"1597200034"},"language":"en","primary_location":{"id":"doi:10.37236/4671","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4671","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p54/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/v22i1p54/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021276189","display_name":"Jorge Alberto Olarte","orcid":"https://orcid.org/0000-0002-1280-1265"},"institutions":[{"id":"https://openalex.org/I4210143738","display_name":"Universidad de Los Andes","ror":"https://ror.org/04pqpvr75","country_code":"BO","type":"education","lineage":["https://openalex.org/I4210143738"]}],"countries":["BO"],"is_corresponding":true,"raw_author_name":"Jorge Alberto Olarte","raw_affiliation_strings":["Universidad de los Andes","Universidad de los Andes;"],"affiliations":[{"raw_affiliation_string":"Universidad de los Andes","institution_ids":["https://openalex.org/I4210143738"]},{"raw_affiliation_string":"Universidad de los Andes;","institution_ids":["https://openalex.org/I4210143738"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5021276189"],"corresponding_institution_ids":["https://openalex.org/I4210143738"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0331941,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.9983999729156494,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9951000213623047,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/flatness","display_name":"Flatness (cosmology)","score":0.8726017475128174},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.8522062301635742},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5696108937263489},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5263895988464355},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4941299259662628},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.48253390192985535},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4241555333137512},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3661210536956787},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2884955108165741},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.26079484820365906},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.12201628088951111},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08991676568984985},{"id":"https://openalex.org/keywords/epistemology","display_name":"Epistemology","score":0.07802566885948181}],"concepts":[{"id":"https://openalex.org/C2778530986","wikidata":"https://www.wikidata.org/wiki/Q5457948","display_name":"Flatness (cosmology)","level":3,"score":0.8726017475128174},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.8522062301635742},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5696108937263489},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5263895988464355},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4941299259662628},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.48253390192985535},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4241555333137512},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3661210536956787},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2884955108165741},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.26079484820365906},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.12201628088951111},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08991676568984985},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.07802566885948181},{"id":"https://openalex.org/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/4671","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4671","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p54/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:1404.4127","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1404.4127","pdf_url":"https://arxiv.org/pdf/1404.4127","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":"pmh:oai:CiteSeerX.psu:10.1.1.751.691","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.751.691","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/1404.4127.pdf","raw_type":"text"},{"id":"doi:10.48550/arxiv.1404.4127","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1404.4127","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-journal"},{"id":"mag:1597200034","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.37236/4671","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4671","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p54/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":[{"score":0.5600000023841858,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1597200034.pdf","grobid_xml":"https://content.openalex.org/works/W1597200034.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W2087066","https://openalex.org/W1847492520","https://openalex.org/W1994595714","https://openalex.org/W2022523090","https://openalex.org/W2047123026","https://openalex.org/W2050070395","https://openalex.org/W2063592986","https://openalex.org/W2063805018","https://openalex.org/W2087138194","https://openalex.org/W2288679103","https://openalex.org/W2990694697"],"related_works":[],"abstract_inverted_index":{"We":[0,30,54,69],"introduce":[1],"the":[2,19,39,47,52,64],"concept":[3,20],"of":[4,12,18,21,49,51,59,73,81],"flatness":[5,22,34,42,78],"degree":[6,35],"for":[7,27,62],"matroids,":[8],"as":[9],"a":[10,60],"generalization":[11],"submodularity.":[13],"This":[14],"represents":[15],"weaker":[16],"variations":[17],"which":[23,37,63],"characterize":[24],"strict":[25],"gammoids":[26,74,87],"finite":[28],"matroids.":[29],"prove":[31],"that":[32,85],"having":[33],"3,":[36],"is":[38,66],"smallest":[40],"non-trivial":[41],"degree,":[43],"implies":[44],"pseudomodularity":[45],"on":[46],"lattice":[48],"flats":[50],"matroid.":[53],"show":[55,71,84],"however":[56],"an":[57],"example":[58],"gammoid":[61],"converse":[65],"not":[67,89],"true.":[68],"also":[70],"examples":[72,83],"with":[75],"each":[76],"possible":[77],"degree.":[79],"All":[80],"this":[82],"pseudomodular":[86],"are":[88],"necessarily":[90],"strict.":[91]},"counts_by_year":[],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}