{"id":"https://openalex.org/W2009444506","doi":"https://doi.org/10.1007/s00454-007-9020-3","title":"Enumeration in Convex Geometries and Associated Polytopal Subdivisions of Spheres","display_name":"Enumeration in Convex Geometries and Associated Polytopal Subdivisions of Spheres","publication_year":2007,"publication_date":"2007-09-12","ids":{"openalex":"https://openalex.org/W2009444506","doi":"https://doi.org/10.1007/s00454-007-9020-3","mag":"2009444506"},"language":"en","primary_location":{"id":"doi:10.1007/s00454-007-9020-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-9020-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-007-9020-3.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 & 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/s00454-007-9020-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008530739","display_name":"Louis J. Billera","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Louis J. Billera","raw_affiliation_strings":["Department of Mathematics, Cornell University, Ithaca, NY, 14853-4201, USA","Cornell University, Department of Mathematics, 14853-4201, Ithaca, NY, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Cornell University, Ithaca, NY, 14853-4201, USA","institution_ids":["https://openalex.org/I205783295"]},{"raw_affiliation_string":"Cornell University, Department of Mathematics, 14853-4201, Ithaca, NY, USA#TAB#","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050340823","display_name":"Samuel K. Hsiao","orcid":null},"institutions":[{"id":"https://openalex.org/I39661318","display_name":"Bard College","ror":"https://ror.org/04yrgt058","country_code":"US","type":"education","lineage":["https://openalex.org/I39661318"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Samuel K. Hsiao","raw_affiliation_strings":["Mathematics Program, Bard College, PO Box 5000, Annandale-on-Hudson, NY, 12504-5000, USA","Bard College, Mathematics Program, PO Box 5000, 12504-5000, Annandale-on-Hudson, NY, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Mathematics Program, Bard College, PO Box 5000, Annandale-on-Hudson, NY, 12504-5000, USA","institution_ids":["https://openalex.org/I39661318"]},{"raw_affiliation_string":"Bard College, Mathematics Program, PO Box 5000, 12504-5000, Annandale-on-Hudson, NY, USA#TAB#","institution_ids":["https://openalex.org/I39661318"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005781105","display_name":"J. Scott Provan","orcid":null},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Scott Provan","raw_affiliation_strings":["Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC, 27599-3260, USA","University of North Carolina, Department of Statistics and Operations Research, PO Box 5000, 27599-3260, Chapel Hill, NC, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC, 27599-3260, USA","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"University of North Carolina, Department of Statistics and Operations Research, PO Box 5000, 27599-3260, Chapel Hill, NC, USA#TAB#","institution_ids":["https://openalex.org/I114027177"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5008530739"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.09828904,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"39","issue":"1-3","first_page":"123","last_page":"137"},"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9952999949455261,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9894000291824341,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7939673662185669},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7720084190368652},{"id":"https://openalex.org/keywords/hyperplane","display_name":"Hyperplane","score":0.6892257332801819},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.6804061532020569},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.6361140608787537},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6070945858955383},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.5880803465843201},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5666865110397339},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5564782023429871},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.48245149850845337},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15522098541259766}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7939673662185669},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7720084190368652},{"id":"https://openalex.org/C68693459","wikidata":"https://www.wikidata.org/wiki/Q657586","display_name":"Hyperplane","level":2,"score":0.6892257332801819},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.6804061532020569},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.6361140608787537},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6070945858955383},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.5880803465843201},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5666865110397339},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5564782023429871},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.48245149850845337},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15522098541259766},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00454-007-9020-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-9020-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-007-9020-3.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 & Computational Geometry","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00454-007-9020-3","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00454-007-9020-3","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00454-007-9020-3.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 & Computational Geometry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.6499999761581421,"display_name":"Sustainable cities and communities"}],"awards":[{"id":"https://openalex.org/G3659375679","display_name":"Enumeration in Graded Posets and Polytopes","funder_award_id":"0100323","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6894402473","display_name":null,"funder_award_id":"Fellowship","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/W2009444506.pdf","grobid_xml":"https://content.openalex.org/works/W2009444506.grobid-xml"},"referenced_works_count":33,"referenced_works":["https://openalex.org/W242841070","https://openalex.org/W1551177513","https://openalex.org/W1556467361","https://openalex.org/W1956653947","https://openalex.org/W1976668598","https://openalex.org/W1983739088","https://openalex.org/W2000597971","https://openalex.org/W2002125379","https://openalex.org/W2005135052","https://openalex.org/W2012691686","https://openalex.org/W2013502334","https://openalex.org/W2034633774","https://openalex.org/W2039415399","https://openalex.org/W2041179721","https://openalex.org/W2061863501","https://openalex.org/W2064838814","https://openalex.org/W2093775888","https://openalex.org/W2109780436","https://openalex.org/W2118624390","https://openalex.org/W2131096251","https://openalex.org/W2146706627","https://openalex.org/W2162305901","https://openalex.org/W2313098266","https://openalex.org/W2499069110","https://openalex.org/W2914659449","https://openalex.org/W2971330320","https://openalex.org/W3102170734","https://openalex.org/W3105819225","https://openalex.org/W4213038708","https://openalex.org/W4232325773","https://openalex.org/W4233224387","https://openalex.org/W4250204379","https://openalex.org/W4256026722"],"related_works":["https://openalex.org/W108845024","https://openalex.org/W4300125793","https://openalex.org/W3023661894","https://openalex.org/W4297887964","https://openalex.org/W2797568024","https://openalex.org/W4297613789","https://openalex.org/W2952440447","https://openalex.org/W2035579007","https://openalex.org/W4298231299","https://openalex.org/W2958361321"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-18T14:38:29.013473","created_date":"2025-10-10T00:00:00"}