{"id":"https://openalex.org/W2294703054","doi":"https://doi.org/10.1080/10586458.2016.1242441","title":"Combinatorial Decompositions, Kirillov\u2013Reshetikhin Invariants, and the Volume Conjecture for Hyperbolic Polyhedra","display_name":"Combinatorial Decompositions, Kirillov\u2013Reshetikhin Invariants, and the Volume Conjecture for Hyperbolic Polyhedra","publication_year":2016,"publication_date":"2016-11-01","ids":{"openalex":"https://openalex.org/W2294703054","doi":"https://doi.org/10.1080/10586458.2016.1242441","mag":"2294703054"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.2016.1242441","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2016.1242441","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1603.02380","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021322556","display_name":"Alexander Kolpakov","orcid":"https://orcid.org/0000-0002-6764-8894"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Alexander Kolpakov","raw_affiliation_strings":["Department of Mathematics, University of Toronto, Toronto, ON, Canada","Department of Mathematics, University of Toronto , Toronto, ON , Canada"],"raw_orcid":"https://orcid.org/0000-0002-6764-8894","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Toronto, Toronto, ON, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Department of Mathematics, University of Toronto , Toronto, ON , Canada","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061984117","display_name":"Jun Murakami","orcid":"https://orcid.org/0000-0001-9869-3383"},"institutions":[{"id":"https://openalex.org/I150744194","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83","country_code":"JP","type":"education","lineage":["https://openalex.org/I150744194"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Jun Murakami","raw_affiliation_strings":["Department of Mathematics, Faculty of Science and Engineering, Waseda University, Tokyo, Japan","Department of Mathematics Faculty of Science and Engineering, Waseda University, Tokyo, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science and Engineering, Waseda University, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]},{"raw_affiliation_string":"Department of Mathematics Faculty of Science and Engineering, Waseda University, Tokyo, Japan","institution_ids":["https://openalex.org/I150744194"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021322556"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.05115681,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"27","issue":"2","first_page":"193","last_page":"207"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9983000159263611,"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"}},"topics":[{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9983000159263611,"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"}},{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9948999881744385,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.9918000102043152,"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/polyhedron","display_name":"Polyhedron","score":0.8513528108596802},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7308288216590881},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6893505454063416},{"id":"https://openalex.org/keywords/volume","display_name":"Volume (thermodynamics)","score":0.5845317244529724},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5825977325439453},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5782514214515686},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.5692194700241089},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5660909414291382},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5073568224906921},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.42460909485816956},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4193156361579895},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4156176447868347},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3355683386325836},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2214210331439972},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18646466732025146},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.1715412437915802},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12877672910690308},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08307752013206482}],"concepts":[{"id":"https://openalex.org/C54829058","wikidata":"https://www.wikidata.org/wiki/Q172937","display_name":"Polyhedron","level":2,"score":0.8513528108596802},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7308288216590881},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6893505454063416},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.5845317244529724},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5825977325439453},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5782514214515686},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.5692194700241089},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5660909414291382},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5073568224906921},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.42460909485816956},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4193156361579895},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4156176447868347},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3355683386325836},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2214210331439972},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18646466732025146},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.1715412437915802},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12877672910690308},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08307752013206482},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1080/10586458.2016.1242441","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.2016.1242441","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:1603.02380","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.02380","pdf_url":"https://arxiv.org/pdf/1603.02380","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":"mag:2294703054","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1603.02380","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-01396113v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01396113","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":"Experimental Mathematics, 2016, pp.1 - 15. &#x27E8;10.1080/10586458.2016.1242441&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1603.02380","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1603.02380","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1603.02380","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1603.02380","pdf_url":"https://arxiv.org/pdf/1603.02380","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/G2478901810","display_name":null,"funder_award_id":"P300P2-151316","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5003018757","display_name":null,"funder_award_id":"KAKENHI 25287014,KAKENHI 25610022,S-14021","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320322638","display_name":"Waseda University","ror":"https://ror.org/00ntfnx83"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2294703054.pdf","grobid_xml":"https://content.openalex.org/works/W2294703054.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W164083653","https://openalex.org/W1554601627","https://openalex.org/W1824336138","https://openalex.org/W1966295071","https://openalex.org/W2043237942","https://openalex.org/W2053808793","https://openalex.org/W2060789956","https://openalex.org/W2072727857","https://openalex.org/W2091944594","https://openalex.org/W2106618694","https://openalex.org/W2155514577","https://openalex.org/W2512327842"],"related_works":["https://openalex.org/W2963880336","https://openalex.org/W3048896198","https://openalex.org/W3161419724","https://openalex.org/W3102396177","https://openalex.org/W2950204560","https://openalex.org/W2460676277","https://openalex.org/W3207632601","https://openalex.org/W2949665016","https://openalex.org/W2114629298","https://openalex.org/W3103912917","https://openalex.org/W2095489530","https://openalex.org/W1790145059","https://openalex.org/W2009145422","https://openalex.org/W3211669461","https://openalex.org/W2135033092","https://openalex.org/W2953048332","https://openalex.org/W2963311888","https://openalex.org/W2100930756","https://openalex.org/W3162927024","https://openalex.org/W2116716322"],"abstract_inverted_index":{"We":[0],"suggest":[1,89],"a":[2,8,26,61,75,130],"method":[3,18,88],"of":[4,23,32,42,69,78,82,97,103,111,121,135,141,145],"computing":[5,107],"volume":[6,68,134],"for":[7,106],"simple":[9],"polytope":[10],"P":[11,24,70,122,136],"in":[12,126],"three-dimensional":[13],"hyperbolic":[14],"space":[15],".":[16],"This":[17],"combines":[19],"the":[20,67,94,101,108,112,117,133,138,142,152],"combinatorial":[21,98],"reduction":[22],"as":[25,151],"trivalent":[27,113],"graph":[28,114],"\u0393":[29],"(the":[30],"1-skeleton":[31],"P)":[33],"by":[34],"I\u2013H,":[35],"or":[36],"Whitehead,":[37],"moves":[38,99,104],"(together":[39],"with":[40,46,86,100],"shrinking":[41],"triangular":[43],"faces)":[44],"aligned":[45],"its":[47],"geometric":[48,119],"splitting":[49],"into":[50],"generalized":[51],"tetrahedra.":[52],"With":[53],"each":[54],"decomposition":[55,120],"(under":[56],"some":[57],"conditions),":[58],"we":[59],"associate":[60,93],"potential":[62],"function":[63],"\u03a6":[64],"such":[65],"that":[66,90],"can":[71],"be":[72,124],"expressed":[73],"through":[74],"critical":[76],"values":[77],"\u03a6.":[79],"The":[80],"results":[81],"our":[83],"numeric":[84],"experiments":[85],"this":[87],"one":[91],"may":[92],"above-mentioned":[95],"sequence":[96,102],"required":[105],"Kirillov\u2013Reshetikhin":[109,143],"invariants":[110,144],"\u0393.":[115],"Then":[116],"corresponding":[118],"might":[123],"used":[125],"order":[127],"to":[128],"establish":[129],"link":[131],"between":[132],"and":[137],"asymptotic":[139],"behavior":[140],"\u0393,":[146],"which":[147],"is":[148],"colloquially":[149],"known":[150],"Volume":[153],"Conjecture.":[154]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-10-10T00:00:00"}
