{"id":"https://openalex.org/W2168397817","doi":"https://doi.org/10.1007/s00454-002-2778-4","title":"In between k -Sets, j -Facets, and i -Faces: (i ,j) - Partitions","display_name":"In between k -Sets, j -Facets, and i -Faces: (i ,j) - Partitions","publication_year":2002,"publication_date":"2002-11-25","ids":{"openalex":"https://openalex.org/W2168397817","doi":"https://doi.org/10.1007/s00454-002-2778-4","mag":"2168397817"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-002-2778-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-2778-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-2778-4.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 and 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/s00454-002-2778-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054003032","display_name":"Artur Andrzejak","orcid":"https://orcid.org/0000-0003-0150-8220"},"institutions":[{"id":"https://openalex.org/I1324840837","display_name":"Hewlett-Packard (United States)","ror":"https://ror.org/059rn9488","country_code":"US","type":"company","lineage":["https://openalex.org/I1324840837"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Artur Andrzejak","raw_affiliation_strings":["Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, CA 94304, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, CA 94304, USA","institution_ids":["https://openalex.org/I1324840837"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5107336010","display_name":"Emo Welzl","orcid":null},"institutions":[{"id":"https://openalex.org/I193291145","display_name":"Schiller International University","ror":"https://ror.org/003tmp461","country_code":"FR","type":"education","lineage":["https://openalex.org/I193291145"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Emo Welzl","raw_affiliation_strings":["Institut fr Theoretische Informatik, ETH Zrich, CH-8092 Zrich, Switzerland","rich,  CH-8092 Z&uuml","Institut f&uuml","r Theoretische Informatik, ETH Z&uuml"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut fr Theoretische Informatik, ETH Zrich, CH-8092 Zrich, Switzerland","institution_ids":["https://openalex.org/I193291145"]},{"raw_affiliation_string":"rich,  CH-8092 Z&uuml","institution_ids":[]},{"raw_affiliation_string":"Institut f&uuml","institution_ids":[]},{"raw_affiliation_string":"r Theoretische Informatik, ETH Z&uuml","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054003032"],"corresponding_institution_ids":["https://openalex.org/I1324840837"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":1.0364,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.83411371,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"29","issue":"1","first_page":"105","last_page":"131"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9922000169754028,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/combinatorics","display_name":"Combinatorics","score":0.871513843536377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8564455509185791},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.6081266403198242},{"id":"https://openalex.org/keywords/general-position","display_name":"General position","score":0.5644937753677368},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5471883416175842},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.5343446135520935},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.4743153750896454},{"id":"https://openalex.org/keywords/finite-set","display_name":"Finite set","score":0.4289875626564026},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.42046108841896057},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.40015909075737},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38413891196250916},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09112474322319031}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.871513843536377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8564455509185791},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6081266403198242},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.5644937753677368},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5471883416175842},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.5343446135520935},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4743153750896454},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4289875626564026},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.42046108841896057},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.40015909075737},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38413891196250916},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09112474322319031},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00454-002-2778-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-2778-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-2778-4.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 and Computational Geometry","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.111.1072","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.111.1072","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.inf.ethz.ch/~emo/PublFiles/ijPartitions_DCG29_03.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.9244","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.9244","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.inf.ethz.ch/~emo/PublFiles/ijPartitions_DCG29_03.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1007/s00454-002-2778-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-002-2778-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-002-2778-4.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 and Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2168397817.pdf","grobid_xml":"https://content.openalex.org/works/W2168397817.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W117619795","https://openalex.org/W1521423805","https://openalex.org/W1539645382","https://openalex.org/W1967705999","https://openalex.org/W1977098616","https://openalex.org/W1980499588","https://openalex.org/W2035298955","https://openalex.org/W2037581698","https://openalex.org/W2041657130","https://openalex.org/W2050230854","https://openalex.org/W2059805293","https://openalex.org/W2094683955","https://openalex.org/W2148642357","https://openalex.org/W2149757010","https://openalex.org/W2161278885","https://openalex.org/W2167816765","https://openalex.org/W2911895609","https://openalex.org/W2914499195","https://openalex.org/W4244525603","https://openalex.org/W4300640952"],"related_works":["https://openalex.org/W2124975081","https://openalex.org/W2139057901","https://openalex.org/W1561087880","https://openalex.org/W2613413781","https://openalex.org/W2054159123","https://openalex.org/W3014659399","https://openalex.org/W4243073496","https://openalex.org/W2101837070","https://openalex.org/W4298712939","https://openalex.org/W1996385391"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}