{"id":"https://openalex.org/W2498879110","doi":"https://doi.org/10.37236/6503","title":"Counting Gluings of Octahedra","display_name":"Counting Gluings of Octahedra","publication_year":2017,"publication_date":"2017-08-25","ids":{"openalex":"https://openalex.org/W2498879110","doi":"https://doi.org/10.37236/6503","mag":"2498879110"},"language":"en","primary_location":{"id":"doi:10.37236/6503","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6503","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/6503","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089238535","display_name":"Valentin Bonzom","orcid":null},"institutions":[{"id":"https://openalex.org/I4210156583","display_name":"Laboratoire d'Informatique de Paris-Nord","ror":"https://ror.org/05g1zjw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210156583","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Valentin Bonzom","raw_affiliation_strings":["LIPN, UMR CNRS 7030, Institut Galil\u00e9e, Universit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9, 99 avenue Jean-Baptiste Cl\u00e9ment, 93430 Villetaneuse, France, EU"],"affiliations":[{"raw_affiliation_string":"LIPN, UMR CNRS 7030, Institut Galil\u00e9e, Universit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9, 99 avenue Jean-Baptiste Cl\u00e9ment, 93430 Villetaneuse, France, EU","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I1294671590","https://openalex.org/I4210156583","https://openalex.org/I4210091437","https://openalex.org/I4210091279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057206217","display_name":"Luca Lionni","orcid":"https://orcid.org/0000-0002-8329-2146"},"institutions":[{"id":"https://openalex.org/I4210109170","display_name":"Laboratoire de Physique Th\u00e9orique","ror":"https://ror.org/01w0hda30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I196454796","https://openalex.org/I4210098836","https://openalex.org/I4210109170","https://openalex.org/I4388446414","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210091279","display_name":"Universit\u00e9 Sorbonne Paris Nord","ror":"https://ror.org/0199hds37","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210091279"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]},{"id":"https://openalex.org/I4210156583","display_name":"Laboratoire d'Informatique de Paris-Nord","ror":"https://ror.org/05g1zjw44","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210156583","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Luca Lionni","raw_affiliation_strings":["Laboratoire de Physique Th\u00e9orique, CNRS UMR 8627, Universit\u00e9 Paris XI, 91405 Orsay Cedex, France, EU and\r\nLIPN, UMR CNRS 7030, Institut Galil\u00e9e, Universit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9, 99 avenue Jean-Baptiste Cl\u00e9ment, 93430 Villetaneuse, France, EU"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique Th\u00e9orique, CNRS UMR 8627, Universit\u00e9 Paris XI, 91405 Orsay Cedex, France, EU and\r\nLIPN, UMR CNRS 7030, Institut Galil\u00e9e, Universit\u00e9 Paris 13, Sorbonne Paris Cit\u00e9, 99 avenue Jean-Baptiste Cl\u00e9ment, 93430 Villetaneuse, France, EU","institution_ids":["https://openalex.org/I204730241","https://openalex.org/I1294671590","https://openalex.org/I4210156583","https://openalex.org/I4210091437","https://openalex.org/I4210091279","https://openalex.org/I4210109170","https://openalex.org/I277688954"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5089238535"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I4210091279","https://openalex.org/I4210091437","https://openalex.org/I4210156583"],"apc_list":null,"apc_paid":null,"fwci":2.38287638,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.83116883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"24","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9998000264167786,"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":0.9998000264167786,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9984999895095825,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/tetrahedron","display_name":"Tetrahedron","score":0.8605124950408936},{"id":"https://openalex.org/keywords/octahedron","display_name":"Octahedron","score":0.8200126886367798},{"id":"https://openalex.org/keywords/bijection","display_name":"Bijection","score":0.8117880821228027},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.8010441064834595},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7104923725128174},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6022375226020813},{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.5711275935173035},{"id":"https://openalex.org/keywords/universality","display_name":"Universality (dynamical systems)","score":0.538176953792572},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17280793190002441},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.15272042155265808},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13442009687423706},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.09285736083984375},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.06593501567840576},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.06466835737228394},{"id":"https://openalex.org/keywords/crystal-structure","display_name":"Crystal structure","score":0.05682837963104248}],"concepts":[{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.8605124950408936},{"id":"https://openalex.org/C198819137","wikidata":"https://www.wikidata.org/wiki/Q188884","display_name":"Octahedron","level":3,"score":0.8200126886367798},{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8117880821228027},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8010441064834595},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7104923725128174},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6022375226020813},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.5711275935173035},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.538176953792572},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17280793190002441},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.15272042155265808},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13442009687423706},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.09285736083984375},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.06593501567840576},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.06466835737228394},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.05682837963104248},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/6503","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6503","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1608.00347","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1608.00347","pdf_url":"https://arxiv.org/pdf/1608.00347","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":"text"},{"id":"mag:2498879110","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1608.00347.pdf","pdf_url":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:HAL:hal-04936116v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04936116","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Electronic Journal of Combinatorics, 2017, 24 (3), pp.P3.36. &#x27E8;10.37236/6503&#x27E9;","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1608.00347","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1608.00347","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.37236/6503","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6503","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1524762130","https://openalex.org/W1579422873","https://openalex.org/W1835385899","https://openalex.org/W1861857255","https://openalex.org/W1966036101","https://openalex.org/W1974956088","https://openalex.org/W2010357160","https://openalex.org/W2023344447","https://openalex.org/W2024285995","https://openalex.org/W2064999608","https://openalex.org/W2068139710","https://openalex.org/W2083916911","https://openalex.org/W2116642797","https://openalex.org/W2139335416","https://openalex.org/W2152460128","https://openalex.org/W2169932795","https://openalex.org/W2300971538","https://openalex.org/W2962960857","https://openalex.org/W2963133037","https://openalex.org/W2994202255","https://openalex.org/W3098716176","https://openalex.org/W3100967813","https://openalex.org/W3101297073","https://openalex.org/W3104174378","https://openalex.org/W3104431390"],"related_works":["https://openalex.org/W2068139710","https://openalex.org/W2396049332","https://openalex.org/W2186128034","https://openalex.org/W2000287066","https://openalex.org/W139605340","https://openalex.org/W3124980558","https://openalex.org/W1520729964","https://openalex.org/W1792333430","https://openalex.org/W2013374592","https://openalex.org/W2331616751","https://openalex.org/W832877322","https://openalex.org/W2464770516","https://openalex.org/W3164450207","https://openalex.org/W1986527413","https://openalex.org/W2150343338","https://openalex.org/W2162775739","https://openalex.org/W3005511372","https://openalex.org/W1970067322","https://openalex.org/W2999504204","https://openalex.org/W2351064274"],"abstract_inverted_index":{"Three-dimensional":[0],"colored":[1,70],"triangulations":[2,60,71],"are":[3,24,88,92,102],"gluings":[4],"of":[5,38,58,81,86,98,112],"tetrahedra":[6,23],"whose":[7],"faces":[8],"carry":[9],"the":[10,19,27,36,79,96,99],"colors":[11],"0,":[12],"1,":[13],"2,":[14],"3":[15],"and":[16,52,91,121],"in":[17,44,107],"which":[18,47,77],"attaching":[20],"maps":[21],"between":[22],"defined":[25],"using":[26,122],"colors.":[28],"This":[29],"framework":[30],"makes":[31],"it":[32],"possible":[33],"to":[34,41,94,105],"generalize":[35],"notion":[37],"two-dimensional":[39],"$2p$-angulations":[40],"three":[42],"dimensions":[43],"a":[45,110],"way":[46],"is":[48,117],"suitable":[49],"for":[50],"combinatorics":[51],"enumeration.":[53],"In":[54],"particular,":[55],"universality":[56],"classes":[57],"three-dimensional":[59],"can":[61],"be":[62,106],"investigated":[63],"within":[64],"this":[65,123],"framework.":[66],"Here":[67],"we":[68],"study":[69],"obtained":[72],"by":[73],"gluing":[74],"octahedra.":[75],"Those":[76],"maximize":[78],"number":[80,85],"edges":[82],"at":[83],"fixed":[84],"octahedra":[87],"fully":[89],"characterized":[90],"shown":[93,104],"have":[95],"topology":[97],"3-sphere.":[100],"They":[101],"further":[103],"bijection":[108],"with":[109],"family":[111],"plane":[113],"trees.":[114],"The":[115],"enumeration":[116],"performed":[118],"both":[119],"directly":[120],"bijection.":[124]},"counts_by_year":[{"year":2019,"cited_by_count":4}],"updated_date":"2026-02-09T09:26:11.010843","created_date":"2025-10-10T00:00:00"}
