{"id":"https://openalex.org/W2964094479","doi":"https://doi.org/10.1137/130913031","title":"A Combinatorial Approach to Colourful Simplicial Depth","display_name":"A Combinatorial Approach to Colourful Simplicial Depth","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2964094479","doi":"https://doi.org/10.1137/130913031","mag":"2964094479"},"language":"en","primary_location":{"id":"doi:10.1137/130913031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130913031","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1212.4720","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004734694","display_name":"Antoine Deza","orcid":"https://orcid.org/0000-0002-2392-4607"},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I4210144804","display_name":"Laboratoire de Recherche en Informatique","ror":"https://ror.org/04e3ktk27","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210144804","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Antoine Deza","raw_affiliation_strings":["Advanced Oprimization Laboratory (Canada)","LRI - Laboratoire de Recherche en Informatique (LRI - B\u00e2timents 650-660 Universit\u00e9 Paris-Sud 91405 Orsay Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Advanced Oprimization Laboratory (Canada)","institution_ids":[]},{"raw_affiliation_string":"LRI - Laboratoire de Recherche en Informatique (LRI - B\u00e2timents 650-660 Universit\u00e9 Paris-Sud 91405 Orsay Cedex - France)","institution_ids":["https://openalex.org/I102197404","https://openalex.org/I4210144804"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101659185","display_name":"Fr\u00e9d\u00e9ric Meunier","orcid":"https://orcid.org/0000-0002-5331-2863"},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Meunier","raw_affiliation_strings":["CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030656730","display_name":"Pauline Sarrabezolles","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pauline Sarrabezolles","raw_affiliation_strings":["CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.13,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.92144269,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"28","issue":"1","first_page":"306","last_page":"322"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9997000098228455,"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":0.9997000098228455,"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":0.996399998664856,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7883986234664917},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7072200775146484},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6797056198120117},{"id":"https://openalex.org/keywords/general-position","display_name":"General position","score":0.6485621929168701},{"id":"https://openalex.org/keywords/octahedron","display_name":"Octahedron","score":0.6107897162437439},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6075369715690613},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.5879844427108765},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5640098452568054},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5188709497451782},{"id":"https://openalex.org/keywords/discrete-geometry","display_name":"Discrete geometry","score":0.4747648239135742},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.45554983615875244},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4362680912017822},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21500736474990845},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.11939319968223572},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.11408984661102295},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10912764072418213},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.05688157677650452}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7883986234664917},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7072200775146484},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6797056198120117},{"id":"https://openalex.org/C150397156","wikidata":"https://www.wikidata.org/wiki/Q591310","display_name":"General position","level":2,"score":0.6485621929168701},{"id":"https://openalex.org/C198819137","wikidata":"https://www.wikidata.org/wiki/Q188884","display_name":"Octahedron","level":3,"score":0.6107897162437439},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6075369715690613},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.5879844427108765},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5640098452568054},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5188709497451782},{"id":"https://openalex.org/C4107886","wikidata":"https://www.wikidata.org/wiki/Q906377","display_name":"Discrete geometry","level":2,"score":0.4747648239135742},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.45554983615875244},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4362680912017822},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21500736474990845},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.11939319968223572},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.11408984661102295},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10912764072418213},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.05688157677650452},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130913031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130913031","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"},{"id":"pmh:oai:arXiv.org:1212.4720","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1212.4720","pdf_url":"https://arxiv.org/pdf/1212.4720","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:HAL:hal-01133440v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01133440","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Discrete Mathematics, 2014, 28 (1), pp.306-322. ⟨10.1137/130913031⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1212.4720","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1212.4720","pdf_url":"https://arxiv.org/pdf/1212.4720","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2964094479.pdf","grobid_xml":"https://content.openalex.org/works/W2964094479.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1893148898","https://openalex.org/W1984879308","https://openalex.org/W1994709142","https://openalex.org/W2001223605","https://openalex.org/W2015695027","https://openalex.org/W2024498264","https://openalex.org/W2025239200","https://openalex.org/W2049678150","https://openalex.org/W2067339112","https://openalex.org/W2089096000","https://openalex.org/W2103307323","https://openalex.org/W2132220587","https://openalex.org/W2171698682","https://openalex.org/W2293156574"],"related_works":["https://openalex.org/W4214593871","https://openalex.org/W2484954041","https://openalex.org/W2081943790","https://openalex.org/W4294585265","https://openalex.org/W2788545171","https://openalex.org/W2117905543","https://openalex.org/W4205122189","https://openalex.org/W3096741285","https://openalex.org/W2468158418","https://openalex.org/W2047989004"],"abstract_inverted_index":{"The":[0,98],"colourful":[1,66,82,95],"simplicial":[2],"depth":[3],"conjecture":[4,44],"states":[5],"that":[6],"any":[7],"point":[8,67,83,96],"in":[9,23,26,30,45,54],"the":[10,43,50],"convex":[11],"hull":[12],"of":[13,15,20,65,75,100],"each":[14,39],"$d+1$":[16,21],"sets,":[17],"or":[18],"colours,":[19],"points":[22],"general":[24],"position":[25],"$\\mathbb{R}^d$":[27],"is":[28,103],"contained":[29],"at":[31],"least":[32],"$d^2+1$":[33],"simplices":[34],"with":[35],"one":[36],"vertex":[37],"from":[38,93],"set.":[40],"We":[41,72],"verify":[42],"dimension":[46],"4":[47],"and":[48,85],"strengthen":[49],"known":[51],"lower":[52],"bounds":[53],"higher":[55],"dimensions.":[56],"These":[57],"results":[58,80],"are":[59],"obtained":[60],"using":[61],"a":[62,94],"combinatorial":[63],"generalization":[64],"configurations":[68,84],"called":[69],"octahedral":[70,76,88,101],"systems.":[71],"present":[73],"properties":[74],"systems":[77,102],"generalizing":[78],"earlier":[79],"on":[81],"exhibit":[86],"an":[87],"system":[89],"which":[90],"cannot":[91],"arise":[92],"configuration.":[97],"number":[99],"also":[104],"given.":[105]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}