{"id":"https://openalex.org/W4402927531","doi":"https://doi.org/10.5070/c64264236","title":"The merging operation and \\((d-i)\\)-simplicial \\(i\\)-simple \\(d\\)-polytopes","display_name":"The merging operation and \\((d-i)\\)-simplicial \\(i\\)-simple \\(d\\)-polytopes","publication_year":2024,"publication_date":"2024-09-27","ids":{"openalex":"https://openalex.org/W4402927531","doi":"https://doi.org/10.5070/c64264236"},"language":"en","primary_location":{"id":"doi:10.5070/c64264236","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c64264236","pdf_url":"https://escholarship.org/content/qt3sf817pd/qt3sf817pd.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://escholarship.org/content/qt3sf817pd/qt3sf817pd.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000152196","display_name":"Isabella Novik","orcid":"https://orcid.org/0000-0003-3695-1337"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Isabella Novik","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5101602928","display_name":"Hailun Zheng","orcid":"https://orcid.org/0000-0001-9914-6218"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hailun Zheng","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5000152196"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13739588,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":"2","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":0.9976000189781189,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9975000023841858,"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/simple","display_name":"Simple (philosophy)","score":0.7564259171485901},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6895912885665894},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6407146453857422},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"Simplicial complex","score":0.517340362071991},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49362432956695557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3352813720703125},{"id":"https://openalex.org/keywords/philosophy","display_name":"Philosophy","score":0.05973884463310242}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7564259171485901},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6895912885665894},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6407146453857422},{"id":"https://openalex.org/C187929450","wikidata":"https://www.wikidata.org/wiki/Q994399","display_name":"Simplicial complex","level":2,"score":0.517340362071991},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49362432956695557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3352813720703125},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.05973884463310242},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5070/c64264236","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c64264236","pdf_url":"https://escholarship.org/content/qt3sf817pd/qt3sf817pd.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt3sf817pd","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/3sf817pd","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"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":"Combinatorial Theory, vol 4, iss 2","raw_type":"article"}],"best_oa_location":{"id":"doi:10.5070/c64264236","is_oa":true,"landing_page_url":"http://dx.doi.org/10.5070/c64264236","pdf_url":"https://escholarship.org/content/qt3sf817pd/qt3sf817pd.pdf","source":{"id":"https://openalex.org/S4210174179","display_name":"Combinatorial Theory","issn_l":"2766-1334","issn":["2766-1334"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorial Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3622234865","display_name":"Combinatorics, Algebra, and Geometry of Simplicial Complexes","funder_award_id":"2246399","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5624041811","display_name":null,"funder_award_id":"DMS-1953815","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7144499314","display_name":"Geometry, Algebra, and Topology of Face Numbers","funder_award_id":"1953815","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G873774507","display_name":"Geometric Combinatorics in Polytopes and Spheres","funder_award_id":"2246739","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/W4402927531.pdf","grobid_xml":"https://content.openalex.org/works/W4402927531.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W4280529077","https://openalex.org/W1493684871","https://openalex.org/W2886567582","https://openalex.org/W4390962314","https://openalex.org/W4289703404","https://openalex.org/W2999175164","https://openalex.org/W4387265813","https://openalex.org/W4286224459","https://openalex.org/W4320410061"],"abstract_inverted_index":{"We":[0,36,58],"define":[1],"a":[2,17,23,27],"certain":[3],"merging":[4],"operation":[5,62],"that":[6,14,38,74,117],"given":[7],"two":[8],"\\(d\\)-polytopes":[9,130],"\\(P\\)":[10,15,45],"and":[11,20,46,87],"\\(Q\\)":[12,21,47],"such":[13],"has":[16,22],"simplex":[18],"facet":[19],"simple":[24],"vertex":[25],"produces":[26],"new":[28,65],"\\(d\\)-polytope":[29],"\\(P":[30,55],"\\triangleright":[31,56],"Q\\)":[32],"with":[33,82,131],"\\(f_0(P)+f_0(Q)-(d+1)\\)":[34],"vertices.":[35],"show":[37,116],"if":[39],"for":[40,75,99,118],"some":[41],"\\(1\\leq":[42],"i\\leq":[43,102],"d-1\\),":[44],"are":[48,123],"\\((d-i)\\)-simplicial":[49,68,95],"\\(i\\)-simple":[50,69,96,112],"\\(d\\)-polytopes,":[51],"then":[52,59],"so":[53],"is":[54,90,105],"Q\\).":[57],"use":[60],"this":[61],"to":[63],"construct":[64],"families":[66],"of":[67,85,94,109,127],"\\(d\\)-polytopes.":[70],"Specifically,":[71],"we":[72,115],"prove":[73],"all":[76,100],"\\(2\\leq":[77,101],"i":[78],"\\leq":[79],"d-2\\leq":[80],"6\\)":[81],"the":[83],"exception":[84],"\\((i,d)=(3,8)\\)":[86],"\\((5,8)\\),":[88],"there":[89,104,122],"an":[91,106],"infinite":[92,107],"family":[93,108],"\\(d\\)-polytopes;":[97],"furthermore,":[98],"4\\),":[103,121],"self-dual":[110,148],"\\(i\\)-simplicial":[111],"\\(2i\\)-polytopes.":[113],"Finally,":[114],"every":[119],"\\(d\\geq":[120],"\\(2^{\\Omega(N)}\\)":[124],"combinatorial":[125],"types":[126],"\\((d-2)\\)-simplicial":[128],"\\(2\\)-simple":[129],"at":[132],"most":[133],"\\(N\\)":[134],"vertices.Mathematics":[135],"Subject":[136],"Classifications:":[137],"52B05,":[138],"52B11Keywords:":[139],"Connected":[140],"sums,":[141],"face":[142,144],"lattice,":[143],"numbers,":[145],"Gosset-Elte":[146],"polytopes,":[147],"polytopes":[149]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
