{"id":"https://openalex.org/W2375830714","doi":"https://doi.org/10.37236/5877","title":"Combinatorics Meets Potential Theory","display_name":"Combinatorics Meets Potential Theory","publication_year":2016,"publication_date":"2016-05-13","ids":{"openalex":"https://openalex.org/W2375830714","doi":"https://doi.org/10.37236/5877","mag":"2375830714"},"language":"en","primary_location":{"id":"doi:10.37236/5877","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5877","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i2p28/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":"preprint","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i2p28/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054280671","display_name":"Philippe D\u2019Arco","orcid":null},"institutions":[{"id":"https://openalex.org/I4210098814","display_name":"UPMC Health System","ror":"https://ror.org/011htkb76","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210098814"]},{"id":"https://openalex.org/I4210097099","display_name":"Institut des Sciences de la Terre de Paris","ror":"https://ror.org/00xagyq07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210097099","https://openalex.org/I4210148025"]}],"countries":["FR","US"],"is_corresponding":true,"raw_author_name":"Philippe D'Arco","raw_affiliation_strings":["UPMC","Institut des Sciences de la Terre de Paris"],"affiliations":[{"raw_affiliation_string":"UPMC","institution_ids":["https://openalex.org/I4210098814"]},{"raw_affiliation_string":"Institut des Sciences de la Terre de Paris","institution_ids":["https://openalex.org/I4210097099"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019818337","display_name":"Valentina Lacivita","orcid":"https://orcid.org/0000-0002-2800-4471"},"institutions":[{"id":"https://openalex.org/I4210098814","display_name":"UPMC Health System","ror":"https://ror.org/011htkb76","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210098814"]},{"id":"https://openalex.org/I4210097099","display_name":"Institut des Sciences de la Terre de Paris","ror":"https://ror.org/00xagyq07","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210097099","https://openalex.org/I4210148025"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Valentina Lacivita","raw_affiliation_strings":["UPMC","Institut des Sciences de la Terre de Paris"],"affiliations":[{"raw_affiliation_string":"UPMC","institution_ids":["https://openalex.org/I4210098814"]},{"raw_affiliation_string":"Institut des Sciences de la Terre de Paris","institution_ids":["https://openalex.org/I4210097099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058536200","display_name":"Sami Mustapha","orcid":"https://orcid.org/0000-0002-7831-0880"},"institutions":[{"id":"https://openalex.org/I4210098814","display_name":"UPMC Health System","ror":"https://ror.org/011htkb76","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210098814"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]}],"countries":["FR","US"],"is_corresponding":false,"raw_author_name":"Sami Mustapha","raw_affiliation_strings":["UPMC","Institut de Math\u00e9matiques de Jussieu"],"affiliations":[{"raw_affiliation_string":"UPMC","institution_ids":["https://openalex.org/I4210098814"]},{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu","institution_ids":["https://openalex.org/I3017942884"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5054280671"],"corresponding_institution_ids":["https://openalex.org/I4210097099","https://openalex.org/I4210098814"],"apc_list":null,"apc_paid":null,"fwci":1.3272,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.77960526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"23","issue":"2","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":0.9584000110626221,"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":0.9584000110626221,"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/T12504","display_name":"Mathematics and Applications","score":0.9573000073432922,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9556999802589417,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.4886682331562042},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4792913794517517}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4886682331562042},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4792913794517517}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/5877","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5877","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i2p28/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-01377735v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01377735","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 (2)","raw_type":"Journal articles"},{"id":"mag:2375830714","is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01377735","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":null,"is_accepted":false,"is_published":null,"raw_source_name":"HAL (Le Centre pour la Communication Scientifique Directe)","raw_type":null}],"best_oa_location":{"id":"doi:10.37236/5877","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5877","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i2p28/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":[{"id":"https://openalex.org/G1404270698","display_name":null,"funder_award_id":"NR-11-IDEX-0004-02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1789083493","display_name":"LABEX pour la mod\u00e9lisation et la simulation scientifiques en recherche","funder_award_id":"ANR-11-LABX-0037","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1817966306","display_name":null,"funder_award_id":"ANR-11-LABX-003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3335229504","display_name":null,"funder_award_id":"Avenir","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3465563395","display_name":null,"funder_award_id":"ANR-11-LABX-0037-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3807293409","display_name":null,"funder_award_id":"ANR-11-LABX-00","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4009746975","display_name":null,"funder_award_id":"ANR-11-IDEX-0004-02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4866930200","display_name":null,"funder_award_id":"ANR-11-IDEX","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5003875507","display_name":null,"funder_award_id":"-11-IDEX-0004-02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5615659713","display_name":null,"funder_award_id":"IDEX-0004-02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6182026652","display_name":null,"funder_award_id":"11-IDEX-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6246589203","display_name":null,"funder_award_id":"11-IDEX-0004-02","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6654833908","display_name":null,"funder_award_id":"ANR-11-IDEX-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7823808512","display_name":null,"funder_award_id":"ANR-11-IDEX-000","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G846706564","display_name":null,"funder_award_id":"ANR-11-IDEX-0004-0","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8668274974","display_name":null,"funder_award_id":"11-LABX-003","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2375830714.pdf","grobid_xml":"https://content.openalex.org/works/W2375830714.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1537670484","https://openalex.org/W1538910591","https://openalex.org/W1640170699","https://openalex.org/W1992543766","https://openalex.org/W1998068293","https://openalex.org/W2010100934","https://openalex.org/W2019718730","https://openalex.org/W2023099303","https://openalex.org/W2028350743","https://openalex.org/W2034324189","https://openalex.org/W2035338904","https://openalex.org/W2051531792","https://openalex.org/W2054431537","https://openalex.org/W2062047199","https://openalex.org/W2068406291","https://openalex.org/W2069419525","https://openalex.org/W2076727031","https://openalex.org/W2081302100","https://openalex.org/W2092923474","https://openalex.org/W2104738412","https://openalex.org/W2139531749","https://openalex.org/W6667386067"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Using":[0],"potential":[1],"theoretic":[2],"techniques,":[3],"we":[4,107],"show":[5],"how":[6],"it":[7],"is":[8,39,86,99],"possible":[9],"to":[10,24,120],"determine":[11],"the":[12,16,25,72,75,92,96,109,115],"dominant":[13],"asymptotics":[14],"for":[15],"number":[17],"of":[18,20,44,74,77,83,104,114],"walks":[19],"length":[21,116],"$n$,":[22],"restricted":[23],"positive":[26],"quadrant":[27],"and":[28,129],"taking":[29],"unit":[30],"steps":[31,52],"in":[32,53,111],"a":[33],"balanced":[34],"set":[35],"$\\Gamma$.":[36],"The":[37,80],"approach":[38,106],"illustrated":[40],"through":[41],"an":[42,102,126],"example":[43],"inhomogeneous":[45],"space":[46],"walk.":[47],"This":[48],"walk":[49],"takes":[50],"its":[51,78],"$\\{":[54,61],"\\leftarrow,":[55,63],"\\uparrow,":[56],"\\rightarrow,":[57,66],"\\downarrow":[58,68],"\\}$":[59],"or":[60],"\\swarrow,":[62],"\\nwarrow,":[64],"\\uparrow,\\nearrow,":[65],"\\searrow,":[67],"\\}$,":[69],"depending":[70],"on":[71],"parity":[73],"coordinates":[76],"positions.":[79],"exponential":[81],"growth":[82,98],"our":[84,105],"model":[85],"$(4\\phi)^n$,":[87],"where":[88],"$\\phi=":[89],"\\frac{1+\\sqrt":[90],"5}{2}$denotes":[91],"Golden":[93],"ratio,":[94],"while":[95],"subexponential":[97],"like":[100],"$1/n$.As":[101],"application":[103],"prove":[108],"non-D-finiteness":[110],"two":[112],"dimensions":[113],"generating":[117],"functions":[118],"corresponding":[119],"nonsingular":[121],"small":[122],"step":[123],"sets":[124],"with":[125],"infinite":[127],"group":[128],"zero-drift.":[130]},"counts_by_year":[{"year":2018,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
