{"id":"https://openalex.org/W1741741233","doi":"https://doi.org/10.37236/4315","title":"Polygons as Sections of Higher-Dimensional Polytopes","display_name":"Polygons as Sections of Higher-Dimensional Polytopes","publication_year":2015,"publication_date":"2015-02-09","ids":{"openalex":"https://openalex.org/W1741741233","doi":"https://doi.org/10.37236/4315","mag":"1741741233"},"language":"en","primary_location":{"id":"doi:10.37236/4315","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4315","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p24/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v22i1p24/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039314003","display_name":"Arnau Padrol","orcid":"https://orcid.org/0000-0003-4747-2729"},"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":"Arnau Padrol","raw_affiliation_strings":["Freie Universit\u00e4t Berlin"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Freie Universit\u00e4t Berlin","institution_ids":["https://openalex.org/I75951250"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024875708","display_name":"Juli\u00e1n Pfeifle","orcid":"https://orcid.org/0000-0001-9777-2602"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Julian Pfeifle","raw_affiliation_strings":["Universitat Polit\u00e8cnica de Catalunya"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universitat Polit\u00e8cnica de Catalunya","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.1994,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.95801527,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"22","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9998000264167786,"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":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"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/T12504","display_name":"Mathematics and Applications","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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9237426519393921},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.9095185995101929},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8181464672088623},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6526041030883789},{"id":"https://openalex.org/keywords/section","display_name":"Section (typography)","score":0.5763177275657654}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9237426519393921},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9095185995101929},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8181464672088623},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6526041030883789},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.5763177275657654},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C112698675","wikidata":"https://www.wikidata.org/wiki/Q37038","display_name":"Advertising","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/4315","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4315","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p24/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:dnet:upcommonspor::c0c0bba3460be523bcfa4671bf65fcfe","is_oa":false,"landing_page_url":"http://hdl.handle.net/2117/86389","pdf_url":null,"source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.37236/4315","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4315","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p24/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G2834789759","display_name":null,"funder_award_id":"SFB/TR 109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G3444685969","display_name":null,"funder_award_id":"TR 109","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6862249499","display_name":null,"funder_award_id":"EUI-EURC-2011-4306","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":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1741741233.pdf"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1534374921","https://openalex.org/W2015290853","https://openalex.org/W2061987651","https://openalex.org/W2066019014","https://openalex.org/W2079335920","https://openalex.org/W2095405086","https://openalex.org/W2107395148","https://openalex.org/W2138677859","https://openalex.org/W2163776721","https://openalex.org/W2248037111","https://openalex.org/W2951633361","https://openalex.org/W3123950972"],"related_works":["https://openalex.org/W4280529077","https://openalex.org/W2560853036","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/W4310904699"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,16,45],"every":[3,17,46],"heptagon":[4],"is":[5],"a":[6,9,26,29,39],"section":[7,27],"of":[8,28,42,51],"$3$-polytope":[10],"with":[11,19,32],"$6$":[12],"vertices.":[13],"This":[14,61],"implies":[15],"$n$-gon":[18],"$n\\geq":[20],"7$":[21],"can":[22],"be":[23],"obtained":[24],"as":[25],"$(2+\\lfloor\\frac{n}{7}\\rfloor)$-dimensional":[30],"polytope":[31],"at":[33],"most":[34],"$\\lceil\\frac{6n}{7}\\rceil$":[35],"vertices;":[36],"and":[37],"provides":[38],"geometric":[40],"proof":[41],"the":[43],"fact":[44],"nonnegative":[47,55],"$n\\times":[48],"m$":[49],"matrix":[50],"rank":[52,56],"$3$":[53],"has":[54,63],"not":[57],"larger":[58],"than":[59],"$\\lceil\\frac{6\\min(n,m)}{7}\\rceil$.":[60],"result":[62],"been":[64],"independently":[65],"proved,":[66],"algebraically,":[67],"by":[68],"Shitov":[69],"(J.":[70],"Combin.":[71],"Theory":[72],"Ser.":[73],"A":[74],"122,":[75],"2014).":[76]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}
