{"id":"https://openalex.org/W2214913906","doi":"https://doi.org/10.37236/5819","title":"Directed Rooted Forests in Higher Dimension","display_name":"Directed Rooted Forests in Higher Dimension","publication_year":2016,"publication_date":"2016-12-09","ids":{"openalex":"https://openalex.org/W2214913906","doi":"https://doi.org/10.37236/5819","mag":"2214913906"},"language":"en","primary_location":{"id":"doi:10.37236/5819","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5819","pdf_url":null,"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://doi.org/10.37236/5819","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065660197","display_name":"Olivier Bernardi","orcid":"https://orcid.org/0000-0003-3231-7152"},"institutions":[{"id":"https://openalex.org/I6902469","display_name":"Brandeis University","ror":"https://ror.org/05abbep66","country_code":"US","type":"education","lineage":["https://openalex.org/I6902469"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Olivier Bernardi","raw_affiliation_strings":["Brandeis University"],"affiliations":[{"raw_affiliation_string":"Brandeis University","institution_ids":["https://openalex.org/I6902469"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018272550","display_name":"Caroline J. Klivans","orcid":null},"institutions":[{"id":"https://openalex.org/I175594653","display_name":"John Brown University","ror":"https://ror.org/02ct41q97","country_code":"US","type":"education","lineage":["https://openalex.org/I175594653"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Caroline J. Klivans","raw_affiliation_strings":["Brown University"],"affiliations":[{"raw_affiliation_string":"Brown University","institution_ids":["https://openalex.org/I175594653"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065660197"],"corresponding_institution_ids":["https://openalex.org/I6902469"],"apc_list":null,"apc_paid":null,"fwci":0.59904354,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.7622261,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"23","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998000264167786,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998000264167786,"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/T11476","display_name":"Graph theory and applications","score":0.9997000098228455,"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/T10086","display_name":"Alzheimer's disease research and treatments","score":0.9926000237464905,"subfield":{"id":"https://openalex.org/subfields/2737","display_name":"Physiology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.726814329624176},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.6952493190765381},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6454946994781494},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.636084258556366},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5895547866821289},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.5136627554893494},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.503274142742157},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3731425404548645},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33449965715408325},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09532710909843445},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07411125302314758}],"concepts":[{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.726814329624176},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.6952493190765381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6454946994781494},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.636084258556366},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5895547866821289},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5136627554893494},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.503274142742157},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3731425404548645},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33449965715408325},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09532710909843445},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07411125302314758},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/5819","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5819","pdf_url":null,"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:1512.07757","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1512.07757","pdf_url":"https://arxiv.org/pdf/1512.07757","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:HAL:hal-01248155v4","is_oa":true,"landing_page_url":"https://hal.science/hal-01248155","pdf_url":null,"source":null,"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2016","raw_type":"Preprints, Working Papers, ..."},{"id":"doi:10.48550/arxiv.1512.07757","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1512.07757","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"},{"id":"mag:2214913906","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:10.37236/5819","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5819","pdf_url":null,"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/15","score":0.7599999904632568,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1434742636","https://openalex.org/W1803417399","https://openalex.org/W1972786753","https://openalex.org/W1989823380","https://openalex.org/W1990905383","https://openalex.org/W2026780596","https://openalex.org/W2060103041","https://openalex.org/W2068537642","https://openalex.org/W2101570837","https://openalex.org/W2128372375","https://openalex.org/W2134506831","https://openalex.org/W2163777132","https://openalex.org/W2963129589","https://openalex.org/W2963465000","https://openalex.org/W2983896310"],"related_works":["https://openalex.org/W2962785277","https://openalex.org/W3094352925","https://openalex.org/W3085558598","https://openalex.org/W2962921265","https://openalex.org/W2990403729","https://openalex.org/W3007278402","https://openalex.org/W2006246904","https://openalex.org/W2950832780","https://openalex.org/W1834206773","https://openalex.org/W2159064170","https://openalex.org/W2950897185","https://openalex.org/W2084230464","https://openalex.org/W1912331361","https://openalex.org/W2053751591","https://openalex.org/W2963879504","https://openalex.org/W3102259363","https://openalex.org/W2177457273","https://openalex.org/W2572452040","https://openalex.org/W2783809158","https://openalex.org/W2169323698"],"abstract_inverted_index":{"For":[0],"a":[1],"graph":[2,27],"$G$,":[3],"the":[4,12,23,26,44],"generating":[5],"function":[6],"of":[7,14,22,25,38,46,56],"rooted":[8,47,59],"forests,":[9],"counted":[10],"by":[11],"number":[13],"connected":[15],"components,":[16],"can":[17],"be":[18],"expressed":[19],"in":[20],"terms":[21],"eigenvalues":[24],"Laplacian.":[28],"We":[29,52],"generalize":[30],"this":[31],"result":[32],"from":[33],"graphs":[34],"to":[35,49,71],"cell":[36],"complexes":[37],"arbitrary":[39],"dimension.":[40,51],"This":[41],"requires":[42],"generalizing":[43],"notion":[45],"forest":[48],"higher":[50,57],"also":[53],"introduce":[54],"orientations":[55,64],"dimensional":[58],"trees":[60],"and":[61],"forests.":[62],"These":[63],"are":[65],"discrete":[66],"vector":[67],"fields":[68],"which":[69],"lead":[70],"open":[72],"questions":[73],"concerning":[74],"expressing":[75],"homological":[76],"quantities":[77],"combinatorially.":[78]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}