{"id":"https://openalex.org/W2072924218","doi":"https://doi.org/10.1137/120894324","title":"From Flag Complexes to Banner Complexes","display_name":"From Flag Complexes to Banner Complexes","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2072924218","doi":"https://doi.org/10.1137/120894324","mag":"2072924218"},"language":"en","primary_location":{"id":"doi:10.1137/120894324","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120894324","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5056971666","display_name":"Steven Klee","orcid":null},"institutions":[{"id":"https://openalex.org/I58610484","display_name":"Seattle University","ror":"https://ror.org/02jqc0m91","country_code":"US","type":"education","lineage":["https://openalex.org/I58610484"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Steven Klee","raw_affiliation_strings":["Seattle University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Seattle University","institution_ids":["https://openalex.org/I58610484"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000152196","display_name":"Isabella Novik","orcid":"https://orcid.org/0000-0003-3695-1337"},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Isabella Novik","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5637,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.6504329,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"27","issue":"2","first_page":"1146","last_page":"1158"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9991999864578247,"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/simplicial-complex","display_name":"Simplicial complex","score":0.9017314910888672},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7837734222412109},{"id":"https://openalex.org/keywords/flag","display_name":"Flag (linear algebra)","score":0.7228144407272339},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7114851474761963},{"id":"https://openalex.org/keywords/banner","display_name":"Banner","score":0.6886575818061829},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4950198531150818},{"id":"https://openalex.org/keywords/codimension","display_name":"Codimension","score":0.48251792788505554},{"id":"https://openalex.org/keywords/abstract-simplicial-complex","display_name":"Abstract simplicial complex","score":0.46111181378364563},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4408246874809265},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3235560655593872},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28383705019950867},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.14345571398735046},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08491101861000061}],"concepts":[{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.9017314910888672},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7837734222412109},{"id":"https://openalex.org/C2776730729","wikidata":"https://www.wikidata.org/wiki/Q1392130","display_name":"Flag (linear algebra)","level":3,"score":0.7228144407272339},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7114851474761963},{"id":"https://openalex.org/C157572991","wikidata":"https://www.wikidata.org/wiki/Q806880","display_name":"Banner","level":2,"score":0.6886575818061829},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4950198531150818},{"id":"https://openalex.org/C83979697","wikidata":"https://www.wikidata.org/wiki/Q1778247","display_name":"Codimension","level":2,"score":0.48251792788505554},{"id":"https://openalex.org/C146867743","wikidata":"https://www.wikidata.org/wiki/Q4669959","display_name":"Abstract simplicial complex","level":3,"score":0.46111181378364563},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4408246874809265},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3235560655593872},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28383705019950867},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.14345571398735046},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08491101861000061},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"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:10.1137/120894324","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120894324","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2445753829","display_name":null,"funder_award_id":"DMS-1069298","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4118861784","display_name":"Around the theory of f-vectors","funder_award_id":"1069298","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1515761639","https://openalex.org/W1532677595","https://openalex.org/W1643680809","https://openalex.org/W1988687684","https://openalex.org/W1989755735","https://openalex.org/W1991238844","https://openalex.org/W2035973405","https://openalex.org/W2041179721","https://openalex.org/W2050846917","https://openalex.org/W2060185552","https://openalex.org/W2086256358","https://openalex.org/W2087239176","https://openalex.org/W2164972130","https://openalex.org/W2211407870","https://openalex.org/W2781179690","https://openalex.org/W2951389159"],"related_works":["https://openalex.org/W2808265377","https://openalex.org/W4288359443","https://openalex.org/W2943582562","https://openalex.org/W2969857904","https://openalex.org/W4206371202","https://openalex.org/W1994441680","https://openalex.org/W4298226481","https://openalex.org/W2952294319","https://openalex.org/W4302397051","https://openalex.org/W2808325035"],"abstract_inverted_index":{"A":[0],"notion":[1],"of":[2,12,20,26,31,34,66,97,104,112],"an":[3,35,67],"$i$-banner":[4,43,57,68,83],"simplicial":[5,28,32,84],"complex":[6,85,91],"is":[7,47,72],"introduced.":[8],"For":[9],"various":[10],"values":[11],"$i$,":[13],"these":[14],"complexes":[15,22,54],"interpolate":[16],"between":[17],"the":[18,24,63,94],"class":[19,25],"flag":[21,53],"and":[23,79,107],"all":[27,75],"complexes.":[29],"Examples":[30],"spheres":[33],"arbitrary":[36],"dimension":[37,105],"that":[38,49],"are":[39,44,61],"$(i+1)$-banner":[40],"but":[41],"not":[42],"constructed.":[45],"It":[46],"shown":[48],"several":[50],"theorems":[51],"for":[52,74,81],"have":[55],"appropriate":[56],"analogues.":[58],"Among":[59],"them":[60],"(1)":[62],"codimension-$(i+j-1)$":[64],"skeleton":[65],"homology":[69],"sphere":[70],"$\\Delta$":[71,86,100],"$2(i+j)$-Cohen--Macaulay":[73],"$0\\leq":[76],"j\\leq":[77],"\\dim\\Delta+1-i$,":[78],"(2)":[80],"every":[82],"there":[87],"exists":[88],"a":[89],"balanced":[90],"$\\Gamma$":[92],"with":[93,110],"same":[95],"number":[96],"vertices":[98],"as":[99],"whose":[101],"face":[102],"numbers":[103],"$i-1$":[106],"higher":[108],"coincide":[109],"those":[111],"$\\Delta$.":[113]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
