{"id":"https://openalex.org/W1634541152","doi":"https://doi.org/10.1007/s00454-018-0041-x","title":"Enumerative Combinatorics of Simplicial and Cell Complexes: Kirchhoff and Trent Type Theorems","display_name":"Enumerative Combinatorics of Simplicial and Cell Complexes: Kirchhoff and Trent Type Theorems","publication_year":2018,"publication_date":"2018-11-26","ids":{"openalex":"https://openalex.org/W1634541152","doi":"https://doi.org/10.1007/s00454-018-0041-x","mag":"1634541152"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-018-0041-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-018-0041-x","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1506.03881","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023198254","display_name":"Sylvain E. Cappell","orcid":"https://orcid.org/0000-0002-5894-5950"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]},{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sylvain E. Cappell","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012-1185, USA","Courant Institute of Mathematical Sciences, New York University New York, USA"],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012-1185, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University New York, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110044546","display_name":"Edward Y. Miller","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Edward Y. Miller","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012-1185, USA","Courant Institute of Mathematical Sciences, New York University New York, USA"],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012-1185, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, New York University New York, USA","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023198254"],"corresponding_institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00522674,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":"1","first_page":"1","last_page":"41"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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":1.0,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9991999864578247,"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/enumerative-combinatorics","display_name":"Enumerative combinatorics","score":0.7159791588783264},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7076079845428467},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5526764392852783},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.5336506962776184},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5182866454124451},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.5041314363479614},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.504059910774231},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4849250614643097},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.47275954484939575},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.40313881635665894},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3767910897731781}],"concepts":[{"id":"https://openalex.org/C112497148","wikidata":"https://www.wikidata.org/wiki/Q336787","display_name":"Enumerative combinatorics","level":2,"score":0.7159791588783264},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7076079845428467},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5526764392852783},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.5336506962776184},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5182866454124451},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.5041314363479614},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.504059910774231},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4849250614643097},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.47275954484939575},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.40313881635665894},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3767910897731781},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00454-018-0041-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00454-018-0041-x","pdf_url":null,"source":{"id":"https://openalex.org/S103671469","display_name":"Discrete & Computational Geometry","issn_l":"0179-5376","issn":["0179-5376","1432-0444"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete & Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1506.03881","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.03881","pdf_url":"https://arxiv.org/pdf/1506.03881","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":null,"raw_type":"text"},{"id":"mag:1634541152","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1506.03881","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":"doi:10.48550/arxiv.1506.03881","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1506.03881","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":"pmh:oai:arXiv.org:1506.03881","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.03881","pdf_url":"https://arxiv.org/pdf/1506.03881","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W121824094","https://openalex.org/W1485072911","https://openalex.org/W1515707356","https://openalex.org/W1534043326","https://openalex.org/W1578099820","https://openalex.org/W1795840257","https://openalex.org/W1843740677","https://openalex.org/W1963885156","https://openalex.org/W1966657789","https://openalex.org/W1978493550","https://openalex.org/W1980379029","https://openalex.org/W2001706704","https://openalex.org/W2045341013","https://openalex.org/W2055476458","https://openalex.org/W2056155661","https://openalex.org/W2060103041","https://openalex.org/W2061116853","https://openalex.org/W2068537642","https://openalex.org/W2074937619","https://openalex.org/W2084667559","https://openalex.org/W2086886817","https://openalex.org/W2087720847","https://openalex.org/W2087992654","https://openalex.org/W2096367125","https://openalex.org/W2096778596","https://openalex.org/W2129636375","https://openalex.org/W2134506831","https://openalex.org/W2319011006","https://openalex.org/W2322220878","https://openalex.org/W2615563936","https://openalex.org/W2616697817","https://openalex.org/W2950965932","https://openalex.org/W2962876363","https://openalex.org/W2963129589","https://openalex.org/W4213378996","https://openalex.org/W4230962939","https://openalex.org/W4237496336","https://openalex.org/W4255288880","https://openalex.org/W4298048726","https://openalex.org/W6603294594"],"related_works":["https://openalex.org/W2963310645","https://openalex.org/W2951060868","https://openalex.org/W2763148572","https://openalex.org/W2963152606","https://openalex.org/W3101735039","https://openalex.org/W426557390","https://openalex.org/W2051690158","https://openalex.org/W595123251","https://openalex.org/W2060103041","https://openalex.org/W3162354407","https://openalex.org/W2631167614","https://openalex.org/W4480325","https://openalex.org/W327529882","https://openalex.org/W2171030144","https://openalex.org/W2963186720","https://openalex.org/W2595918272","https://openalex.org/W2679288235","https://openalex.org/W2327133656","https://openalex.org/W2758576888","https://openalex.org/W3123107397"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}