{"id":"https://openalex.org/W2949373715","doi":"https://doi.org/10.1080/10586458.2019.1641766","title":"Topological Prismatoids and Small Simplicial Spheres of Large Diameter","display_name":"Topological Prismatoids and Small Simplicial Spheres of Large Diameter","publication_year":2019,"publication_date":"2019-07-22","ids":{"openalex":"https://openalex.org/W2949373715","doi":"https://doi.org/10.1080/10586458.2019.1641766","mag":"2949373715"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2019.1641766","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2019.1641766","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental 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/1807.03030","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Francisco Criado","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Francisco Criado","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"last","author":{"id":null,"display_name":"Francisco Santos","orcid":"https://orcid.org/0000-0003-2120-9068"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Francisco Santos","raw_affiliation_strings":["Departamento de Matem\u00e1ticas, Estad\u00edstica y Computaci\u00f3n, Universidad de Cantabria, Santander, Spain"],"raw_orcid":"https://orcid.org/0000-0003-2120-9068","affiliations":[{"raw_affiliation_string":"Departamento de Matem\u00e1ticas, Estad\u00edstica y Computaci\u00f3n, Universidad de Cantabria, Santander, Spain","institution_ids":["https://openalex.org/I13134134"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.9505,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83890374,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"31","issue":"2","first_page":"461","last_page":"473"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.6434000134468079,"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":0.6434000134468079,"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":0.13840000331401825,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.05139999836683273,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.7010999917984009},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6531000137329102},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6266000270843506},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.6241999864578247},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4993000030517578},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.4641999900341034},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.39959999918937683}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.821399986743927},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.7010999917984009},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6531000137329102},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6266000270843506},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6241999864578247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6046000123023987},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4993000030517578},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.4641999900341034},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.39959999918937683},{"id":"https://openalex.org/C118539577","wikidata":"https://www.wikidata.org/wiki/Q3402784","display_name":"Combinatorial proof","level":2,"score":0.39010000228881836},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.3197000026702881},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.29190000891685486},{"id":"https://openalex.org/C2778478883","wikidata":"https://www.wikidata.org/wiki/Q7825025","display_name":"Topological complexity","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C145054310","wikidata":"https://www.wikidata.org/wiki/Q212803","display_name":"Algebraic topology","level":3,"score":0.27709999680519104},{"id":"https://openalex.org/C4107886","wikidata":"https://www.wikidata.org/wiki/Q906377","display_name":"Discrete geometry","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C127634017","wikidata":"https://www.wikidata.org/wiki/Q5627866","display_name":"h-vector","level":3,"score":0.26570001244544983},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2565999925136566}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/10586458.2019.1641766","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2019.1641766","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1807.03030","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.03030","pdf_url":"https://arxiv.org/pdf/1807.03030","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":null,"raw_type":"text"},{"id":"pmh:oai:repositorio.unican.es:10902/27811","is_oa":true,"landing_page_url":"https://hdl.handle.net/10902/27811","pdf_url":"https://repositorio.unican.es/xmlui/bitstream/10902/27811/2/TopologicalPrismatoidsSmal.pdf","source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Experimental Mathematics, 2022, 31(2), 461-473","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1807.03030","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1807.03030","pdf_url":"https://arxiv.org/pdf/1807.03030","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":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4290799699","display_name":null,"funder_award_id":"MTM2017-83750-P","funder_id":"https://openalex.org/F4320323688","funder_display_name":"Einstein Stiftung Berlin"},{"id":"https://openalex.org/G7370262331","display_name":null,"funder_award_id":"EVF-2015-230","funder_id":"https://openalex.org/F4320323688","funder_display_name":"Einstein Stiftung Berlin"}],"funders":[{"id":"https://openalex.org/F4320323688","display_name":"Einstein Stiftung Berlin","ror":"https://ror.org/03s0fv852"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1486393174","https://openalex.org/W1853367770","https://openalex.org/W1966042529","https://openalex.org/W1966068899","https://openalex.org/W1992051521","https://openalex.org/W2012903160","https://openalex.org/W2030718802","https://openalex.org/W2048994963","https://openalex.org/W2050088862","https://openalex.org/W2086847284","https://openalex.org/W2117921017","https://openalex.org/W2124010812","https://openalex.org/W2151888904","https://openalex.org/W2233474732","https://openalex.org/W2592711915","https://openalex.org/W2947196409","https://openalex.org/W2963980320","https://openalex.org/W4230167402"],"related_works":[],"abstract_inverted_index":{"We":[0,24],"introduce":[1],"topological":[2,62],"prismatoids,":[3],"a":[4],"combinatorial":[5,45,78],"abstraction":[6],"of":[7,71],"the":[8,14,21,27,52,69,81,89],"(geometric)":[9],"prismatoids":[10,40,63],"recently":[11],"introduced":[12],"by":[13,93],"second":[15],"author":[16],"to":[17,20,33],"construct":[18,34,56],"counter-examples":[19],"Hirsch":[22,82],"conjecture.":[23],"show":[25],"that":[26,31,88],"\"strong":[28],"d-step":[29],"Theorem\"":[30],"allows":[32],"such":[35],"large-diameter":[36],"polytopes":[37],"from":[38],"\"non-d-step\"":[39],"still":[41],"works":[42],"at":[43],"this":[44],"level.":[46],"Then,":[47],"using":[48],"metaheuristic":[49],"methods":[50],"on":[51],"flip":[53],"graph,":[54],"we":[55,109],"four":[57],"combinatorially":[58],"different":[59],"non-d-step":[60],"4-dimensional":[61],"with":[64,74],"14":[65],"vertices.":[66],"This":[67],"implies":[68],"existence":[70],"8-dimensional":[72],"spheres":[73,105],"18":[75],"vertices":[76],"whose":[77],"diameter":[79],"exceeds":[80],"bound.":[83],"These":[84],"examples":[85,92],"are":[86,106,115],"smaller":[87],"previously":[90],"known":[91],"Mani":[94],"and":[95],"Walkup":[96],"in":[97],"1980":[98],"(24":[99],"vertices,":[100],"dimension":[101],"11).":[102],"Our":[103],"non-Hirsch":[104],"shellable":[107],"but":[108],"do":[110],"not":[111],"know":[112],"whether":[113],"they":[114],"realizable":[116],"as":[117],"polytopes.":[118]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2019-06-27T00:00:00"}