{"id":"https://openalex.org/W1879658246","doi":"https://doi.org/10.37236/1818","title":"Flag Vectors of Multiplicial Polytopes","display_name":"Flag Vectors of Multiplicial Polytopes","publication_year":2004,"publication_date":"2004-09-20","ids":{"openalex":"https://openalex.org/W1879658246","doi":"https://doi.org/10.37236/1818","mag":"1879658246"},"language":"en","primary_location":{"id":"doi:10.37236/1818","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1818","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r65/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/v11i1r65/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086353661","display_name":"Margaret M. Bayer","orcid":"https://orcid.org/0000-0002-8519-5438"},"institutions":[{"id":"https://openalex.org/I146416000","display_name":"University of Kansas","ror":"https://ror.org/001tmjg57","country_code":"US","type":"education","lineage":["https://openalex.org/I146416000"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Margaret M. Bayer","raw_affiliation_strings":["Department of Mathematics University of Kansas Lawrence, KS 66045-7523, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Kansas Lawrence, KS 66045-7523, USA","institution_ids":["https://openalex.org/I146416000"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086353661"],"corresponding_institution_ids":["https://openalex.org/I146416000"],"apc_list":null,"apc_paid":null,"fwci":0.3388,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61276365,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9987000226974487,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9973999857902527,"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/T12504","display_name":"Mathematics and Applications","score":0.9872999787330627,"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/polytope","display_name":"Polytope","score":0.9604545831680298},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8730310201644897},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.785130500793457},{"id":"https://openalex.org/keywords/flag","display_name":"Flag (linear algebra)","score":0.7466590404510498},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5691633820533752},{"id":"https://openalex.org/keywords/simplex","display_name":"Simplex","score":0.5458552837371826},{"id":"https://openalex.org/keywords/facet","display_name":"Facet (psychology)","score":0.4357069134712219},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3209495544433594},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.11956673860549927},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.07802864909172058}],"concepts":[{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.9604545831680298},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8730310201644897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.785130500793457},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.7466590404510498},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5691633820533752},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.5458552837371826},{"id":"https://openalex.org/C43122875","wikidata":"https://www.wikidata.org/wiki/Q5428522","display_name":"Facet (psychology)","level":4,"score":0.4357069134712219},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3209495544433594},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.11956673860549927},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.07802864909172058},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C187288502","wikidata":"https://www.wikidata.org/wiki/Q641118","display_name":"Personality","level":2,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C2865642","wikidata":"https://www.wikidata.org/wiki/Q378132","display_name":"Big Five personality traits","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1818","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1818","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r65/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.75.9822","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.75.9822","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_11/PDF/v11i1r65.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.77.7331","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.77.7331","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_11/PostScriptfiles/v11i1r65.ps","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/1818","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1818","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r65/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/G2582482343","display_name":null,"funder_award_id":"DMS-9810361","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8496220283","display_name":"Mathematical Sciences Research Institute","funder_award_id":"9810361","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/W1879658246.pdf","grobid_xml":"https://content.openalex.org/works/W1879658246.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1579678295","https://openalex.org/W1912474658","https://openalex.org/W1963521086","https://openalex.org/W1971425931","https://openalex.org/W1978185251","https://openalex.org/W2034658974","https://openalex.org/W2093254591","https://openalex.org/W2248285095","https://openalex.org/W2914471578"],"related_works":["https://openalex.org/W4297449612","https://openalex.org/W1642182499","https://openalex.org/W3105548266","https://openalex.org/W1976967559","https://openalex.org/W2963459254","https://openalex.org/W2018146720","https://openalex.org/W4286870264","https://openalex.org/W4299550417","https://openalex.org/W2279275934","https://openalex.org/W4304687059"],"abstract_inverted_index":{"Bisztriczky":[0],"introduced":[1],"the":[2,8,27,52,61,82,85],"multiplex":[3],"as":[4],"a":[5,57,77,102,116,120],"generalization":[6,59],"of":[7,30,42,51,60,67,84,112,122],"simplex.":[9],"A":[10,39],"polytope":[11],"is":[12,24,49,73,104],"multiplicial":[13,31,43,108],"if":[14],"all":[15],"its":[16],"faces":[17],"are":[18,56,70],"multiplexes.":[19],"In":[20,100],"this":[21],"paper":[22],"it":[23],"proved":[25],"that":[26],"flag":[28,65],"vectors":[29,66],"polytopes":[32,69,109],"depend":[33],"only":[34],"on":[35,115],"their":[36,113],"face":[37],"vectors.":[38],"special":[40],"class":[41],"polytopes,":[44],"also":[45],"discovered":[46],"by":[47],"Bisztriczky,":[48],"comprised":[50],"ordinary":[53,68,86],"polytopes.":[54,63],"These":[55],"natural":[58],"cyclic":[62],"The":[64],"determined.":[71],"This":[72],"used":[74],"to":[75],"give":[76],"surprisingly":[78],"simple":[79],"formula":[80],"for":[81,97,106],"$h$-vector":[83],"$d$-polytope":[87],"with":[88],"$n+1$":[89],"vertices":[90,114],"and":[91],"characteristic":[92],"$k$:":[93],"$h_i={k-d+i\\choose":[94],"i}+(n-k){k-d+i-1\\choose":[95],"i-1}$,":[96],"$i\\le":[98],"d/2$.":[99],"addition,":[101],"construction":[103],"given":[105],"4-dimensional":[107],"having":[110],"two-thirds":[111],"single":[117],"facet,":[118],"answering":[119],"question":[121],"Bisztriczky.":[123]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}