{"id":"https://openalex.org/W4408537631","doi":"https://doi.org/10.1007/s00493-025-00138-2","title":"The Signed Varchenko Determinant for Complexes of Oriented Matroids","display_name":"The Signed Varchenko Determinant for Complexes of Oriented Matroids","publication_year":2025,"publication_date":"2025-03-17","ids":{"openalex":"https://openalex.org/W4408537631","doi":"https://doi.org/10.1007/s00493-025-00138-2"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-025-00138-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00138-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00138-2.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00138-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045347494","display_name":"Winfried Hochst\u00e4ttler","orcid":"https://orcid.org/0000-0001-7344-7143"},"institutions":[{"id":"https://openalex.org/I120691247","display_name":"University of Hagen","ror":"https://ror.org/04tkkr536","country_code":"DE","type":"education","lineage":["https://openalex.org/I120691247"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Winfried Hochst\u00e4ttler","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik und Informatik, FernUniversit\u00e4t in Hagen, 58084, Hagen, Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, FernUniversit\u00e4t in Hagen, 58084, Hagen, Germany","institution_ids":["https://openalex.org/I120691247"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039694281","display_name":"Sophia Keip","orcid":"https://orcid.org/0000-0002-8524-5132"},"institutions":[{"id":"https://openalex.org/I120691247","display_name":"University of Hagen","ror":"https://ror.org/04tkkr536","country_code":"DE","type":"education","lineage":["https://openalex.org/I120691247"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sophia Keip","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik und Informatik, FernUniversit\u00e4t in Hagen, 58084, Hagen, Germany"],"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik und Informatik, FernUniversit\u00e4t in Hagen, 58084, Hagen, Germany","institution_ids":["https://openalex.org/I120691247"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057566451","display_name":"Kolja Knauer","orcid":"https://orcid.org/0000-0002-8151-2184"},"institutions":[{"id":"https://openalex.org/I71999127","display_name":"Universitat de Barcelona","ror":"https://ror.org/021018s57","country_code":"ES","type":"education","lineage":["https://openalex.org/I71999127"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Kolja Knauer","raw_affiliation_strings":["Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Departament de Matem\u00e0tiques i Inform\u00e0tica, Universitat de Barcelona, Barcelona, Spain","institution_ids":["https://openalex.org/I71999127"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045347494"],"corresponding_institution_ids":["https://openalex.org/I120691247"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09895833,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"2","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":0.9945999979972839,"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":0.9945999979972839,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9939000010490417,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.9879000186920166,"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/matroid","display_name":"Matroid","score":0.883556604385376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8271692991256714},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7560040950775146}],"concepts":[{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.883556604385376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8271692991256714},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7560040950775146}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00493-025-00138-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00138-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00138-2.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00493-025-00138-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00138-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00138-2.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4408537631.pdf"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1970512471","https://openalex.org/W2030621045","https://openalex.org/W2067320522","https://openalex.org/W2803058183","https://openalex.org/W2962840653","https://openalex.org/W2962867705","https://openalex.org/W2964111989","https://openalex.org/W3207904795","https://openalex.org/W4254205555","https://openalex.org/W4386789998"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2058299944","https://openalex.org/W4233892543","https://openalex.org/W1550144461","https://openalex.org/W4323360720","https://openalex.org/W2783959783","https://openalex.org/W2037206237","https://openalex.org/W2540764814","https://openalex.org/W3000635646","https://openalex.org/W2033011390"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"generalize":[2],"the":[3],"(signed)":[4],"Varchenko":[5],"matrix":[6],"of":[7,13],"a":[8,22],"hyperplane":[9,30],"arrangement":[10],"to":[11],"complexes":[12],"oriented":[14,33],"matroids":[15],"and":[16,32],"show":[17],"that":[18],"its":[19],"determinant":[20],"has":[21],"nice":[23],"factorization.":[24],"This":[25],"extends":[26],"previous":[27],"results":[28],"on":[29],"arrangements":[31],"matroids.":[34]},"counts_by_year":[],"updated_date":"2025-12-21T23:12:01.093139","created_date":"2025-10-10T00:00:00"}
