{"id":"https://openalex.org/W2160176903","doi":"https://doi.org/10.1007/s00493-003-0026-z","title":"Inequalities for cd -Indices of Joins and Products of Polytopes","display_name":"Inequalities for cd -Indices of Joins and Products of Polytopes","publication_year":2003,"publication_date":"2003-07-01","ids":{"openalex":"https://openalex.org/W2160176903","doi":"https://doi.org/10.1007/s00493-003-0026-z","mag":"2160176903"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-003-0026-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-003-0026-z","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070448622","display_name":"Richard Ehrenborg","orcid":"https://orcid.org/0000-0001-5854-3890"},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Richard Ehrenborg","raw_affiliation_strings":["Department of Mathematics, University of Kentucky, Lexington, KY, 40506-0027, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kentucky, Lexington, KY, 40506-0027, USA","institution_ids":["https://openalex.org/I143302722"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031672897","display_name":"Harold H. Fox","orcid":null},"institutions":[{"id":"https://openalex.org/I1343180700","display_name":"Intel (United States)","ror":"https://ror.org/01ek73717","country_code":"US","type":"company","lineage":["https://openalex.org/I1343180700"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Harold Fox","raw_affiliation_strings":["Artifical Intelligence Lab, MIT, Cambridge, MA, 02139, USA"],"affiliations":[{"raw_affiliation_string":"Artifical Intelligence Lab, MIT, Cambridge, MA, 02139, USA","institution_ids":["https://openalex.org/I1343180700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070448622"],"corresponding_institution_ids":["https://openalex.org/I143302722"],"apc_list":null,"apc_paid":null,"fwci":2.7506,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.90005023,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"3","first_page":"427","last_page":"452"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998999834060669,"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":0.9998999834060669,"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9983000159263611,"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/T11716","display_name":"Random Matrices and Applications","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/polytope","display_name":"Polytope","score":0.9134441614151001},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8578860759735107},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8498719334602356},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.8462110757827759},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5179385542869568},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.48385465145111084},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.4511153995990753},{"id":"https://openalex.org/keywords/flag","display_name":"Flag (linear algebra)","score":0.43855318427085876},{"id":"https://openalex.org/keywords/joins","display_name":"Joins","score":0.4236987829208374},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34262484312057495},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.17198693752288818},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14326128363609314},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09746140241622925}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9134441614151001},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8578860759735107},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8498719334602356},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.8462110757827759},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5179385542869568},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.48385465145111084},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.4511153995990753},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.43855318427085876},{"id":"https://openalex.org/C2778692605","wikidata":"https://www.wikidata.org/wiki/Q4041866","display_name":"Joins","level":2,"score":0.4236987829208374},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34262484312057495},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.17198693752288818},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14326128363609314},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09746140241622925},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00493-003-0026-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00493-003-0026-z","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.92.2578","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.92.2578","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ms.uky.edu/~jrge/Papers/Mixing.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W84695432","https://openalex.org/W1500084468","https://openalex.org/W1517150618","https://openalex.org/W1565240535","https://openalex.org/W1584718768","https://openalex.org/W1971731613","https://openalex.org/W1990911204","https://openalex.org/W1994397976","https://openalex.org/W2008933953","https://openalex.org/W2009479830","https://openalex.org/W2013502334","https://openalex.org/W2050134666","https://openalex.org/W2054009182","https://openalex.org/W2103911131","https://openalex.org/W2109780436","https://openalex.org/W2155851113","https://openalex.org/W2334336952","https://openalex.org/W3152105221"],"related_works":["https://openalex.org/W2324035390","https://openalex.org/W2088925915","https://openalex.org/W2695311495","https://openalex.org/W3175137310","https://openalex.org/W2382891957","https://openalex.org/W2393491644","https://openalex.org/W3034984450","https://openalex.org/W4287022798","https://openalex.org/W2884061808","https://openalex.org/W2901329027"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}