{"id":"https://openalex.org/W2906839665","doi":"https://doi.org/10.48550/arxiv.1901.00668","title":"Directed Plateau Polyhypercubes","display_name":"Directed Plateau Polyhypercubes","publication_year":2019,"publication_date":"2019-01-03","ids":{"openalex":"https://openalex.org/W2906839665","doi":"https://doi.org/10.48550/arxiv.1901.00668","mag":"2906839665"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1901.00668","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.00668","pdf_url":"https://arxiv.org/pdf/1901.00668","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1901.00668","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037036020","display_name":"Abderrahim Arabi","orcid":"https://orcid.org/0000-0002-1962-6957","observed_orcids":["https://orcid.org/0000-0002-1962-6957"]},"institutions":[{"id":"https://openalex.org/I157169809","display_name":"University of Sciences and Technology Houari Boumediene","ror":"https://ror.org/02kb89c09","country_code":"DZ","type":"education","lineage":["https://openalex.org/I157169809"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Arabi, Abderrahim","raw_affiliation_strings":["USTHB , Faculty of Mathematics RECITS Laboratory BP 32 , El Alia 16111 , Bab Ezzouar Algiers , Algeria","University of Science and Technology Houari Boumediene#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"USTHB , Faculty of Mathematics RECITS Laboratory BP 32 , El Alia 16111 , Bab Ezzouar Algiers , Algeria","institution_ids":["https://openalex.org/I157169809"]},{"raw_affiliation_string":"University of Science and Technology Houari Boumediene#TAB#","institution_ids":["https://openalex.org/I157169809"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054807235","display_name":"Hac\u00e8ne Belbachir","orcid":"https://orcid.org/0000-0001-8540-3033","observed_orcids":["https://orcid.org/0000-0001-8540-3033"]},"institutions":[{"id":"https://openalex.org/I157169809","display_name":"University of Sciences and Technology Houari Boumediene","ror":"https://ror.org/02kb89c09","country_code":"DZ","type":"education","lineage":["https://openalex.org/I157169809"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Belbachir, Hac\u00e8ne","raw_affiliation_strings":["USTHB , Faculty of Mathematics RECITS Laboratory BP 32 , El Alia 16111 , Bab Ezzouar Algiers , Algeria","University of Science and Technology Houari Boumediene#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"USTHB , Faculty of Mathematics RECITS Laboratory BP 32 , El Alia 16111 , Bab Ezzouar Algiers , Algeria","institution_ids":["https://openalex.org/I157169809"]},{"raw_affiliation_string":"University of Science and Technology Houari Boumediene#TAB#","institution_ids":["https://openalex.org/I157169809"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026325097","display_name":"Jean-Philippe Dubernard","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210108118","display_name":"Laboratoire d'Informatique, du Traitement de l'Information et des Syst\u00e8mes","ror":"https://ror.org/01f1vfy95","country_code":"FR","type":"facility","lineage":["https://openalex.org/I141576021","https://openalex.org/I4210105918","https://openalex.org/I4210108118","https://openalex.org/I62396329","https://openalex.org/I88814501"]},{"id":"https://openalex.org/I62396329","display_name":"Universit\u00e9 de Rouen Normandie","ror":"https://ror.org/03nhjew95","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I62396329"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Dubernard, Jean-Philippe","raw_affiliation_strings":["University of Rouen-Normandie , Faculty of Science and Technique LITIS Laboratory Avenue de l'universit\u00e9 76800 Saint-\u00c9tienne-du-Rouvray Rouen , France","University of Rouen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Rouen-Normandie , Faculty of Science and Technique LITIS Laboratory Avenue de l'universit\u00e9 76800 Saint-\u00c9tienne-du-Rouvray Rouen , France","institution_ids":["https://openalex.org/I4210108118","https://openalex.org/I62396329"]},{"raw_affiliation_string":"University of Rouen","institution_ids":["https://openalex.org/I62396329"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9994999766349792,"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":0.9994999766349792,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/width","display_name":"width","score":0.7210000157356262},{"id":"https://openalex.org/keywords/generating-functions","display_name":"generating functions","score":0.6800000071525574}],"concepts":[{"id":"https://openalex.org/C2780030769","wikidata":"https://www.wikidata.org/wiki/Q4968575","display_name":"Plateau (mathematics)","level":2,"score":0.8693104386329651},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6880399584770203},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.6376206874847412},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5956880450248718},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5557036399841309},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.45317935943603516},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3924846351146698},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3801630437374115},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26803523302078247},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18269950151443481},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.05465862154960632},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.04487943649291992},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:1901.00668","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.00668","pdf_url":"https://arxiv.org/pdf/1901.00668","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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:2906839665","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1901.00668","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.1901.00668","doi":"https://doi.org/10.48550/arxiv.1901.00668","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1901.00668","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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:1901.00668","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1901.00668","pdf_url":"https://arxiv.org/pdf/1901.00668","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1490173767","https://openalex.org/W1543194273","https://openalex.org/W2004056472","https://openalex.org/W2006207441","https://openalex.org/W2036252950","https://openalex.org/W2076114468","https://openalex.org/W2094062181","https://openalex.org/W2108781459","https://openalex.org/W2395156691","https://openalex.org/W2551867718","https://openalex.org/W2900496983"],"related_works":["https://openalex.org/W2950502494"],"abstract_inverted_index":{"In":[0],"this":[1,46],"paper,":[2],"we":[3,36],"study":[4],"a":[5,24],"particular":[6],"family":[7],"of":[8,41],"polyhypercubes":[9],"in":[10,45],"dimension":[11],"$d\\geq":[12],"3$,":[13],"the":[14,21,27,42],"directed":[15],"plateau":[16],"polyhypercubes,":[17],"according":[18],"to":[19,20],"width":[22],"and":[23,35],"new":[25],"parameter":[26],"lateral":[28],"area.":[29],"We":[30],"give":[31],"an":[32,39],"explicit":[33],"formula":[34],"also":[37],"propose":[38],"expression":[40],"generating":[43],"function":[44],"case.":[47]},"counts_by_year":[],"updated_date":"2026-10-06T10:28:23.643775","created_date":"2025-10-10T00:00:00"}