{"id":"https://openalex.org/W2280463100","doi":"https://doi.org/10.37236/4350","title":"On Computation of Baker and Norine\u2019s Rank on Complete Graphs","display_name":"On Computation of Baker and Norine\u2019s Rank on Complete Graphs","publication_year":2016,"publication_date":"2016-02-19","ids":{"openalex":"https://openalex.org/W2280463100","doi":"https://doi.org/10.37236/4350","mag":"2280463100"},"language":"en","primary_location":{"id":"doi:10.37236/4350","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4350","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p31/pdf","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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p31/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040359504","display_name":"Robert Cori","orcid":"https://orcid.org/0000-0001-9776-1196"},"institutions":[{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Robert Cori","raw_affiliation_strings":["Labri, Universit\u00e9 Bordeaux 1"],"affiliations":[{"raw_affiliation_string":"Labri, Universit\u00e9 Bordeaux 1","institution_ids":["https://openalex.org/I4210142254"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010460422","display_name":"Yvan Le Borgne","orcid":null},"institutions":[{"id":"https://openalex.org/I4210160189","display_name":"Institut Polytechnique de Bordeaux","ror":"https://ror.org/054qv7y42","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210160189"]},{"id":"https://openalex.org/I15057530","display_name":"Universit\u00e9 de Bordeaux","ror":"https://ror.org/057qpr032","country_code":"FR","type":"education","lineage":["https://openalex.org/I15057530"]},{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Yvan Le Borgne","raw_affiliation_strings":["Labri Universit\u00e9 Bordeaux"],"affiliations":[{"raw_affiliation_string":"Labri Universit\u00e9 Bordeaux","institution_ids":["https://openalex.org/I4210142254","https://openalex.org/I15057530","https://openalex.org/I4210160189"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5040359504"],"corresponding_institution_ids":["https://openalex.org/I4210142254"],"apc_list":null,"apc_paid":null,"fwci":4.5838,"has_fulltext":true,"cited_by_count":14,"citation_normalized_percentile":{"value":0.94056988,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"23","issue":"1","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":0.9980000257492065,"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":0.9980000257492065,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9909999966621399,"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"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/catalan-number","display_name":"Catalan number","score":0.7220981121063232},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7202396988868713},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.6334693431854248},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5381866693496704},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.537548303604126},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.48243626952171326},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4393709897994995},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.4102494716644287},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15562570095062256}],"concepts":[{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.7220981121063232},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7202396988868713},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.6334693431854248},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5381866693496704},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.537548303604126},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.48243626952171326},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4393709897994995},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.4102494716644287},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15562570095062256},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/4350","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4350","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p31/pdf","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:HAL:hal-01416914v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01416914","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":"The Electronic Journal of Combinatorics, 2016, 23","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.37236/4350","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4350","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p31/pdf","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2280463100.pdf","grobid_xml":"https://content.openalex.org/works/W2280463100.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W56906882","https://openalex.org/W594004768","https://openalex.org/W812206059","https://openalex.org/W1485445902","https://openalex.org/W1544535863","https://openalex.org/W1557368527","https://openalex.org/W1602252920","https://openalex.org/W1910083634","https://openalex.org/W1964453615","https://openalex.org/W1975077105","https://openalex.org/W1984208049","https://openalex.org/W1987008489","https://openalex.org/W2013190996","https://openalex.org/W2018695682","https://openalex.org/W2025847513","https://openalex.org/W2034224223","https://openalex.org/W2037190943","https://openalex.org/W2049916150","https://openalex.org/W2066653142","https://openalex.org/W2074094342","https://openalex.org/W2075514521","https://openalex.org/W2083387674","https://openalex.org/W2121699196","https://openalex.org/W2140545974","https://openalex.org/W2144978102","https://openalex.org/W2148260769","https://openalex.org/W2225144138","https://openalex.org/W2604805256","https://openalex.org/W2752061190","https://openalex.org/W2950659266","https://openalex.org/W2951875774","https://openalex.org/W2952303299","https://openalex.org/W2963299389","https://openalex.org/W2964022551","https://openalex.org/W2993224395","https://openalex.org/W3101379151","https://openalex.org/W4239240946","https://openalex.org/W4294222131","https://openalex.org/W4294328963","https://openalex.org/W4297229520","https://openalex.org/W4302072811","https://openalex.org/W6628947489"],"related_works":["https://openalex.org/W4253699484","https://openalex.org/W2612136637","https://openalex.org/W2033428949","https://openalex.org/W2937076924","https://openalex.org/W3167464145","https://openalex.org/W4210335754","https://openalex.org/W2017381362","https://openalex.org/W2888257356","https://openalex.org/W2924584751","https://openalex.org/W4381712798"],"abstract_inverted_index":{"The":[0,59,106],"paper":[1,82],"by":[2,168],"M.":[3],"Baker":[4,207],"and":[5,18,50,67,133,159,179,208],"S.":[6],"Norine":[7,209],"in":[8,23,53,71,77,112,210],"2007":[9],"introduced":[10],"a":[11,20,45,74,113,149,163,169,175,180,183],"new":[12,21,124],"parameter":[13,125,132,135],"on":[14,57,65],"configurations":[15,56,94],"of":[16,26,48,55,90,93,108,110,117,152,177,189,192,203,206],"graphs":[17,27,41,66],"gave":[19],"result":[22,35],"the":[24,68,88,91,96,129,134,154,193,204],"theory":[25],"which":[28,126,165],"has":[29,102],"an":[30,85,122,138,200],"algebraic":[31],"geometry":[32],"flavor.":[33],"This":[34,100,131],"was":[36],"called":[37,61],"Riemann-Roch":[38],"formula":[39],"for":[40,87,95],"since":[42],"it":[43],"defines":[44],"combinatorial":[46,212],"version":[47,116],"divisors":[49],"their":[51],"ranks":[52],"terms":[54],"graphs.":[58],"so":[60],"chip":[62],"firing":[63],"game":[64],"sandpile":[69],"model":[70],"physics":[72],"play":[73],"central":[75],"role":[76],"this":[78,81,118],"theory.":[79],"In":[80,196],"we":[83,127,198],"present":[84],"algorithm":[86,101,119],"determination":[89],"rank":[92,160],"complete":[97],"graph":[98],"$K_n$.":[99],"linear":[103],"arithmetic":[104],"complexity.":[105],"analysis":[107],"number":[109],"iterations":[111],"less":[114],"optimized":[115],"leads":[120],"to":[121,141,148,162,174],"apparently":[123],"call":[128],"prerank.":[130],"dinv":[136],"provide":[137],"alternative":[139,201],"description":[140],"some":[142],"well":[143],"known":[144],"$q,t$-Catalan":[145],"numbers.":[146,195],"Restricted":[147],"natural":[150,156],"subset":[151],"configurations,":[153],"two":[155,187],"statistics":[157],"degree":[158],"lead":[161],"distribution":[164],"is":[166,182],"described":[167],"generating":[170],"function":[171],"which,":[172],"up":[173],"change":[176],"variables":[178],"rescaling,":[181],"symmetric":[184],"fraction":[185],"involving":[186],"copies":[188],"Carlitz":[190],"$q$-analogue":[191],"Catalan":[194],"annex,":[197],"give":[199],"presentation":[202],"theorem":[205],"purely":[211],"terms.":[213]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}