{"id":"https://openalex.org/W1993114066","doi":"https://doi.org/10.1017/s0963548314000340","title":"On Irreducible Maps and Slices","display_name":"On Irreducible Maps and Slices","publication_year":2014,"publication_date":"2014-07-09","ids":{"openalex":"https://openalex.org/W1993114066","doi":"https://doi.org/10.1017/s0963548314000340","mag":"1993114066"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548314000340","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548314000340","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1303.3728","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080082247","display_name":"J\u00e9r\u00e9mie Bouttier","orcid":"https://orcid.org/0000-0003-3852-155X"},"institutions":[{"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/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I29607241","display_name":"\u00c9cole Normale Sup\u00e9rieure - PSL","ror":"https://ror.org/05a0dhs15","country_code":"FR","type":"other","lineage":["https://openalex.org/I2746051580","https://openalex.org/I29607241"]},{"id":"https://openalex.org/I4210127506","display_name":"D\u00e9partement de math\u00e9matiques et applications","ror":"https://ror.org/03k9z2963","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210127506"]},{"id":"https://openalex.org/I4210163633","display_name":"Institut de Physique Th\u00e9orique","ror":"https://ror.org/058rvd314","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2738703131","https://openalex.org/I2738703131","https://openalex.org/I4210098836","https://openalex.org/I4210113668","https://openalex.org/I4210163633"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"J. BOUTTIER","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matiques et Applications, \u00c9cole Normale Sup\u00e9rieure, 45 Rue d'Ulm, F-75231 Paris Cedex 05","Institut de Physique Th\u00e9orique, CEA, IPhT, F-91191 Gif-sur-Yvette, France, CNRS, URA 2306 (e-mails:","Institut de Physique Th\u00e9orique - UMR CNRS 3681","D\u00e9partement de Math\u00e9matiques et Applications - ENS Paris"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques et Applications, \u00c9cole Normale Sup\u00e9rieure, 45 Rue d'Ulm, F-75231 Paris Cedex 05","institution_ids":["https://openalex.org/I29607241","https://openalex.org/I4210127506"]},{"raw_affiliation_string":"Institut de Physique Th\u00e9orique, CEA, IPhT, F-91191 Gif-sur-Yvette, France, CNRS, URA 2306 (e-mails:","institution_ids":["https://openalex.org/I4210163633","https://openalex.org/I2738703131","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Institut de Physique Th\u00e9orique - UMR CNRS 3681","institution_ids":["https://openalex.org/I4210163633","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matiques et Applications - ENS Paris","institution_ids":["https://openalex.org/I2746051580","https://openalex.org/I4210127506","https://openalex.org/I29607241"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055644587","display_name":"Emmanuel Guitter","orcid":"https://orcid.org/0000-0003-1447-5886"},"institutions":[{"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/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I4210163633","display_name":"Institut de Physique Th\u00e9orique","ror":"https://ror.org/058rvd314","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2738703131","https://openalex.org/I2738703131","https://openalex.org/I4210098836","https://openalex.org/I4210113668","https://openalex.org/I4210163633"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"E. GUITTER","raw_affiliation_strings":["Institut de Physique Th\u00e9orique, CEA, IPhT, F-91191 Gif-sur-Yvette, France, CNRS, URA 2306 (e-mails:","Institut de Physique Th\u00e9orique,CEA,IPhT,F-91191 Gif-sur-Yvette,France,CNRS,URA 2306("],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Physique Th\u00e9orique, CEA, IPhT, F-91191 Gif-sur-Yvette, France, CNRS, URA 2306 (e-mails:","institution_ids":["https://openalex.org/I4210163633","https://openalex.org/I2738703131","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Institut de Physique Th\u00e9orique,CEA,IPhT,F-91191 Gif-sur-Yvette,France,CNRS,URA 2306(","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080082247"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I2738703131","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I4210127506","https://openalex.org/I4210163633"],"apc_list":null,"apc_paid":null,"fwci":1.4681,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.8163218,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"6","first_page":"914","last_page":"972"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9973000288009644,"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"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9973000288009644,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9972000122070312,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.991100013256073,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/bijection","display_name":"Bijection","score":0.8385459184646606},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6097041368484497},{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.49550068378448486},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4898376166820526},{"id":"https://openalex.org/keywords/face","display_name":"Face (sociological concept)","score":0.47987452149391174},{"id":"https://openalex.org/keywords/irreducible-representation","display_name":"Irreducible representation","score":0.47335290908813477},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.471482515335083},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.44117990136146545},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42578384280204773},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37499767541885376},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13809621334075928}],"concepts":[{"id":"https://openalex.org/C24424167","wikidata":"https://www.wikidata.org/wiki/Q180907","display_name":"Bijection","level":2,"score":0.8385459184646606},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6097041368484497},{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.49550068378448486},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4898376166820526},{"id":"https://openalex.org/C2779304628","wikidata":"https://www.wikidata.org/wiki/Q3503480","display_name":"Face (sociological concept)","level":2,"score":0.47987452149391174},{"id":"https://openalex.org/C142292226","wikidata":"https://www.wikidata.org/wiki/Q13690522","display_name":"Irreducible representation","level":2,"score":0.47335290908813477},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.471482515335083},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.44117990136146545},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42578384280204773},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37499767541885376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13809621334075928},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C36289849","wikidata":"https://www.wikidata.org/wiki/Q34749","display_name":"Social science","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0963548314000340","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548314000340","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1303.3728","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.3728","pdf_url":"https://arxiv.org/pdf/1303.3728","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-00801674v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00801674","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorics, Probability and Computing, 2014, 23, pp.914-972. ⟨10.1017/S0963548314000340⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1303.3728","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.3728","pdf_url":"https://arxiv.org/pdf/1303.3728","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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W186403072","https://openalex.org/W1498113475","https://openalex.org/W1595602558","https://openalex.org/W1813708725","https://openalex.org/W1846834076","https://openalex.org/W1938588645","https://openalex.org/W1988101899","https://openalex.org/W1996008071","https://openalex.org/W1996648614","https://openalex.org/W2007151050","https://openalex.org/W2014724230","https://openalex.org/W2021355739","https://openalex.org/W2030285167","https://openalex.org/W2032246347","https://openalex.org/W2034983981","https://openalex.org/W2042456974","https://openalex.org/W2044557831","https://openalex.org/W2059657531","https://openalex.org/W2073442617","https://openalex.org/W2075345390","https://openalex.org/W2079265093","https://openalex.org/W2082705126","https://openalex.org/W2083520497","https://openalex.org/W2089947338","https://openalex.org/W2099777423","https://openalex.org/W2103025659","https://openalex.org/W2117234194","https://openalex.org/W2130519984","https://openalex.org/W2328363074","https://openalex.org/W2340541605","https://openalex.org/W2911361414","https://openalex.org/W2949076455","https://openalex.org/W2950093039","https://openalex.org/W2950253680","https://openalex.org/W2962961940","https://openalex.org/W3100230559","https://openalex.org/W3100883954","https://openalex.org/W3104039994","https://openalex.org/W3104703509","https://openalex.org/W4212799367","https://openalex.org/W6629928517","https://openalex.org/W6658940258"],"related_works":["https://openalex.org/W4288805235","https://openalex.org/W2952259524","https://openalex.org/W1508013399","https://openalex.org/W1630536276","https://openalex.org/W2104153156","https://openalex.org/W1988994151","https://openalex.org/W2083385887","https://openalex.org/W2141770429","https://openalex.org/W1990462962","https://openalex.org/W2362128619"],"abstract_inverted_index":{"We":[0,41,109,125],"consider":[1],"the":[2,32,47,81,92,146],"problem":[3],"of":[4,14,28,34,37,63,95,114,120,136,148],"enumerating":[5],"d":[6,21,30,39,65,96,115,122],"-irreducible":[7,97,116],"maps,":[8],"i.e.":[9],",":[10,22],"planar":[11],"maps":[12,54,59,82,98,130],"all":[13,64],"whose":[15],"cycles":[16],"have":[17],"length":[18,29],"at":[19],"least":[20],"and":[23,70],"such":[24],"that":[25,128],"any":[26],"cycle":[27],"is":[31],"boundary":[33],"a":[35,61,71,134],"face":[36,101],"degree":[38],".":[40],"develop":[42],"two":[43],"approaches":[44],"in":[45,79,104,118,145],"parallel:":[46],"natural":[48],"approach":[49,73],"via":[50,74],"substitution,":[51],"where":[52],"these":[53],"are":[55],"obtained":[56],"from":[57],"general":[58],"by":[60,67],"replacement":[62],"-cycles":[66],"elementary":[68],"faces,":[69],"bijective":[72],"slice":[75],"decomposition,":[76],"which":[77,140],"consists":[78],"cutting":[80],"along":[83],"shortest":[84],"paths.":[85],"Both":[86],"lead":[87],"to":[88,133],"explicit":[89],"expressions":[90],"for":[91],"generating":[93],"functions":[94],"with":[99],"controlled":[100],"degrees,":[102],"summarized":[103],"some":[105],"elegant":[106],"\u2018pointing":[107],"formula\u2019.":[108],"provide":[110],"an":[111],"equivalent":[112],"description":[113],"slices":[117],"terms":[119],"so-called":[121],"-oriented":[123],"trees.":[124,151],"finally":[126],"show":[127],"irreducible":[129],"give":[131],"rise":[132],"hierarchy":[135],"discrete":[137],"integrable":[138],"equations":[139,142],"include":[141],"encountered":[143],"previously":[144],"context":[147],"naturally":[149],"embedded":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2026-05-17T08:19:37.847499","created_date":"2025-10-10T00:00:00"}