{"id":"https://openalex.org/W1867676345","doi":"https://doi.org/10.37236/3315","title":"Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs","display_name":"Face Numbers of Centrally Symmetric Polytopes Produced from Split Graphs","publication_year":2013,"publication_date":"2013-05-16","ids":{"openalex":"https://openalex.org/W1867676345","doi":"https://doi.org/10.37236/3315","mag":"1867676345"},"language":"en","primary_location":{"id":"doi:10.37236/3315","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3315","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p32/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5079294052","display_name":"Ragnar Freij-Hollanti","orcid":"https://orcid.org/0000-0001-8156-2053"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Ragnar Freij","raw_affiliation_strings":["Department of Mathematics and Systems Analysis\r\nAalto University\r\nEspoo, Finland","Department of Mathematics and Systems Analysis#R##N#Aalto University#R##N#Espoo, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Systems Analysis\r\nAalto University\r\nEspoo, Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Department of Mathematics and Systems Analysis#R##N#Aalto University#R##N#Espoo, Finland","institution_ids":["https://openalex.org/I9927081"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111642117","display_name":"Matthias Henze","orcid":null},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthias Henze","raw_affiliation_strings":["Institut f\u00fcr Informatik\r\nFreie Universit\u00e4t Berlin\r\nBerlin, Germany","Institut f\u00fcr Informatik#R##N#Freie Universit\u00e4t Berlin#R##N#Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik\r\nFreie Universit\u00e4t Berlin\r\nBerlin, Germany","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Institut f\u00fcr Informatik#R##N#Freie Universit\u00e4t Berlin#R##N#Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073660295","display_name":"Moritz W. Schmitt","orcid":null},"institutions":[{"id":"https://openalex.org/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Moritz W. Schmitt","raw_affiliation_strings":["Institut f\u00fcr Mathematik\r\nFreie Universit\u00e4t Berlin\r\nBerlin, Germany","Institut f\u00fcr Mathematik#R##N#Freie Universit\u00e4t Berlin#R##N#Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik\r\nFreie Universit\u00e4t Berlin\r\nBerlin, Germany","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik#R##N#Freie Universit\u00e4t Berlin#R##N#Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]},{"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/I75951250","display_name":"Freie Universit\u00e4t Berlin","ror":"https://ror.org/046ak2485","country_code":"DE","type":"education","lineage":["https://openalex.org/I75951250"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"G\u00fcnter M. Ziegler","raw_affiliation_strings":["Institut f\u00fcr Mathematik\r\nFreie Universit\u00e4t Berlin\r\nBerlin, Germany","Institut f\u00fcr Mathematik#R##N#Freie Universit\u00e4t Berlin#R##N#Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik\r\nFreie Universit\u00e4t Berlin\r\nBerlin, Germany","institution_ids":["https://openalex.org/I75951250"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematik#R##N#Freie Universit\u00e4t Berlin#R##N#Berlin, Germany","institution_ids":["https://openalex.org/I75951250"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5079294052"],"corresponding_institution_ids":["https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":1.165,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.71886121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","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":1.0,"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":1.0,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.9847000241279602,"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/polytope","display_name":"Polytope","score":0.9607128500938416},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8755291700363159},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7535281181335449},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7042524814605713},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5686731338500977},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.53334641456604},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3287777304649353},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08107981085777283}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9607128500938416},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8755291700363159},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7535281181335449},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7042524814605713},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5686731338500977},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.53334641456604},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3287777304649353},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08107981085777283},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/3315","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3315","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/3315","is_oa":true,"landing_page_url":"https://doi.org/10.37236/3315","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p32/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4946944115","display_name":null,"funder_award_id":"Matheon","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6024419964","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G762232396","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1867676345.pdf","grobid_xml":"https://content.openalex.org/works/W1867676345.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1570340896","https://openalex.org/W1597196612","https://openalex.org/W2054249726","https://openalex.org/W2233474732","https://openalex.org/W2271049245","https://openalex.org/W2282893942","https://openalex.org/W2531904221","https://openalex.org/W3099537220","https://openalex.org/W4297399141"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W2507185596","https://openalex.org/W1493684871","https://openalex.org/W4286224459","https://openalex.org/W2886567582","https://openalex.org/W4289703404","https://openalex.org/W4387265813","https://openalex.org/W3103454236","https://openalex.org/W4320410061","https://openalex.org/W2999175164"],"abstract_inverted_index":{"We":[0,15],"analyze":[1],"a":[2,52],"remarkable":[3],"class":[4],"of":[5,12,55],"centrally":[6],"symmetric":[7],"polytopes,":[8],"the":[9,34],"Hansen":[10,56],"polytopes":[11,22,36,57],"split":[13],"graphs.":[14,48],"confirm":[16],"Kalai's":[17],"$3^d$":[18,28,42],"conjecture":[19],"for":[20],"such":[21],"(they":[23],"all":[24],"have":[25,40,59],"at":[26],"least":[27],"nonempty":[29,43,62],"faces)":[30,44],"and":[31],"show":[32],"that":[33,58],"Hanner":[35],"among":[37],"them":[38],"(which":[39],"exactly":[41],"correspond":[45],"to":[46],"threshold":[47],"Our":[49],"study":[50],"produces":[51],"new":[53],"family":[54],"only":[60],"$3^d+16$":[61],"faces.":[63]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-03-12T08:34:05.389933","created_date":"2025-10-10T00:00:00"}