{"id":"https://openalex.org/W1997625405","doi":"https://doi.org/10.1007/bf02187790","title":"Hyperplane arrangements with a lattice of regions","display_name":"Hyperplane arrangements with a lattice of regions","publication_year":1990,"publication_date":"1990-06-01","ids":{"openalex":"https://openalex.org/W1997625405","doi":"https://doi.org/10.1007/bf02187790","mag":"1997625405"},"language":"en","primary_location":{"id":"doi:10.1007/bf02187790","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02187790","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02187790.pdf","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 &amp; Computational Geometry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/BF02187790.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024148075","display_name":"Anders Bj\u00f6rner","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Anders Bj\u00f6rner","raw_affiliation_strings":["Department of Mathematics, Royal Institute of Technology, 10044, Stockholm, Sweden","Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden 10044#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Royal Institute of Technology, 10044, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]},{"raw_affiliation_string":"Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden 10044#TAB#","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056740759","display_name":"Paul H. Edelman","orcid":"https://orcid.org/0000-0001-6963-347X"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Paul H. Edelman","raw_affiliation_strings":["School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA","School of Mathematics, University of Minnesota, Minneapolis, USA 55455#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"School of Mathematics, University of Minnesota, Minneapolis, USA 55455#TAB#","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055917631","display_name":"G\u00fcnter M. Ziegler","orcid":"https://orcid.org/0000-0003-1502-1915"},"institutions":[{"id":"https://openalex.org/I119916105","display_name":"Augsburg University","ror":"https://ror.org/057ewhh68","country_code":"US","type":"education","lineage":["https://openalex.org/I119916105"]},{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"G\u00fcnter M. Ziegler","raw_affiliation_strings":["Department of Mathematics, Augsburg University, 8900, Augsburg, Germany","Department of Mathematics, Augsburg University, Augsburg, Germany 8900#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Augsburg University, 8900, Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]},{"raw_affiliation_string":"Department of Mathematics, Augsburg University, Augsburg, Germany 8900#TAB#","institution_ids":["https://openalex.org/I119916105"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":5.1138,"has_fulltext":true,"cited_by_count":130,"citation_normalized_percentile":{"value":0.95581897,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"5","issue":"3","first_page":"263","last_page":"288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T11797","display_name":"graph theory and CDMA systems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11830","display_name":"Point processes and geometric inequalities","score":0.9635000228881836,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/partially-ordered-set","display_name":"Partially ordered set","score":0.8705823421478271},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.8412314653396606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7912895679473877},{"id":"https://openalex.org/keywords/matroid","display_name":"Matroid","score":0.7627304792404175},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7624555230140686},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6057412028312683},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.5654051303863525},{"id":"https://openalex.org/keywords/hasse-diagram","display_name":"Hasse diagram","score":0.5347183346748352},{"id":"https://openalex.org/keywords/abstract-simplicial-complex","display_name":"Abstract simplicial complex","score":0.5265151262283325},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.4808136224746704},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4480043053627014}],"concepts":[{"id":"https://openalex.org/C180645754","wikidata":"https://www.wikidata.org/wiki/Q474715","display_name":"Partially ordered set","level":2,"score":0.8705823421478271},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.8412314653396606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7912895679473877},{"id":"https://openalex.org/C106286213","wikidata":"https://www.wikidata.org/wiki/Q898572","display_name":"Matroid","level":2,"score":0.7627304792404175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7624555230140686},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6057412028312683},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.5654051303863525},{"id":"https://openalex.org/C140002607","wikidata":"https://www.wikidata.org/wiki/Q901446","display_name":"Hasse diagram","level":3,"score":0.5347183346748352},{"id":"https://openalex.org/C146867743","wikidata":"https://www.wikidata.org/wiki/Q4669959","display_name":"Abstract simplicial complex","level":3,"score":0.5265151262283325},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.4808136224746704},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4480043053627014},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/bf02187790","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02187790","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02187790.pdf","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 &amp; Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:16245","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/16245","pdf_url":null,"source":{"id":"https://openalex.org/S4377196968","display_name":"Publication Server OPUS (University of Augsburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I179225836","host_organization_name":"University of Augsburg","host_organization_lineage":["https://openalex.org/I179225836"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/bf02187790","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bf02187790","pdf_url":"https://link.springer.com/content/pdf/10.1007/BF02187790.pdf","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 &amp; Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.44999998807907104,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G2075240676","display_name":"Mathematical Sciences: Combinatorics: Enumeration and Posets","funder_award_id":"8700995","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2435971554","display_name":"Mathematical Sciences: Combinatorial Aspects of Dissections of n-Space by Hyper- planes","funder_award_id":"8612446","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1997625405.pdf","grobid_xml":"https://content.openalex.org/works/W1997625405.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W93565887","https://openalex.org/W112702794","https://openalex.org/W650639416","https://openalex.org/W1546959834","https://openalex.org/W1607402086","https://openalex.org/W1965060262","https://openalex.org/W1972166787","https://openalex.org/W1985302945","https://openalex.org/W2005742663","https://openalex.org/W2006899318","https://openalex.org/W2012226462","https://openalex.org/W2024000612","https://openalex.org/W2026159747","https://openalex.org/W2029787168","https://openalex.org/W2031773577","https://openalex.org/W2038844190","https://openalex.org/W2039415399","https://openalex.org/W2055584434","https://openalex.org/W2057258003","https://openalex.org/W2062291935","https://openalex.org/W2074536752","https://openalex.org/W2086297027","https://openalex.org/W2095094581","https://openalex.org/W2313098266","https://openalex.org/W2405154940","https://openalex.org/W3159824982","https://openalex.org/W4212938248","https://openalex.org/W4242999670"],"related_works":["https://openalex.org/W2368666440","https://openalex.org/W2135545610","https://openalex.org/W1608104040","https://openalex.org/W2952147592","https://openalex.org/W2063945525","https://openalex.org/W2134937349","https://openalex.org/W1984174158","https://openalex.org/W4299987152","https://openalex.org/W4313646714","https://openalex.org/W3104305163"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
