{"id":"https://openalex.org/W1523717544","doi":"https://doi.org/10.37236/1800","title":"Sur une G\u00e9n\u00e9ralisation des Coefficients Binomiaux","display_name":"Sur une G\u00e9n\u00e9ralisation des Coefficients Binomiaux","publication_year":2004,"publication_date":"2004-07-26","ids":{"openalex":"https://openalex.org/W1523717544","doi":"https://doi.org/10.37236/1800","mag":"1523717544"},"language":"en","primary_location":{"id":"doi:10.37236/1800","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1800","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r47/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":null,"license_id":null,"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/v11i1r47/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5112447300","display_name":"Fr\u00e9d\u00e9ric Jouhet","orcid":null},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Fr\u00e9d\u00e9ric Jouhet","raw_affiliation_strings":["Institut Girard Desargues, Universit Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France","Institut Girard Desargues, Universit\u00e9 Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France"],"affiliations":[{"raw_affiliation_string":"Institut Girard Desargues, Universit Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France","institution_ids":["https://openalex.org/I100532134"]},{"raw_affiliation_string":"Institut Girard Desargues, Universit\u00e9 Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France","institution_ids":["https://openalex.org/I100532134"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052442829","display_name":"Bodo Lass","orcid":null},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Bodo Lass","raw_affiliation_strings":["Institut Girard Desargues, Universit Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France","Institut Girard Desargues, Universit\u00e9 Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France"],"affiliations":[{"raw_affiliation_string":"Institut Girard Desargues, Universit Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France","institution_ids":["https://openalex.org/I100532134"]},{"raw_affiliation_string":"Institut Girard Desargues, Universit\u00e9 Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France","institution_ids":["https://openalex.org/I100532134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108363298","display_name":"Jiang Zeng","orcid":"https://orcid.org/0000-0002-7063-1882"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jiang Zeng","raw_affiliation_strings":["Institut Girard Desargues, Universit Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France","Institut Girard Desargues, Universit\u00e9 Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France"],"affiliations":[{"raw_affiliation_string":"Institut Girard Desargues, Universit Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France","institution_ids":["https://openalex.org/I100532134"]},{"raw_affiliation_string":"Institut Girard Desargues, Universit\u00e9 Claude Bernard (Lyon 1) 43, bd du 11 Novembre 1918, 69622 Villeurbanne cedex, France","institution_ids":["https://openalex.org/I100532134"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112447300"],"corresponding_institution_ids":["https://openalex.org/I100532134"],"apc_list":null,"apc_paid":null,"fwci":0.5058,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.56646217,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","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":0.9998000264167786,"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":0.9998000264167786,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.998199999332428,"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"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","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/mathematics","display_name":"Mathematics","score":0.9458064436912537},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7049952745437622},{"id":"https://openalex.org/keywords/binomial-coefficient","display_name":"Binomial coefficient","score":0.6930817365646362},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6660763025283813},{"id":"https://openalex.org/keywords/binomial","display_name":"Binomial (polynomial)","score":0.5566930770874023},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.5239329934120178},{"id":"https://openalex.org/keywords/interpretation","display_name":"Interpretation (philosophy)","score":0.5179623365402222},{"id":"https://openalex.org/keywords/gaussian-binomial-coefficient","display_name":"Gaussian binomial coefficient","score":0.5010628700256348},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4231472313404083},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3471181392669678},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.32856839895248413},{"id":"https://openalex.org/keywords/negative-binomial-distribution","display_name":"Negative binomial distribution","score":0.14857640862464905},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1287420094013214},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12474942207336426}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9458064436912537},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7049952745437622},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.6930817365646362},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6660763025283813},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.5566930770874023},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.5239329934120178},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.5179623365402222},{"id":"https://openalex.org/C139505817","wikidata":"https://www.wikidata.org/wiki/Q5527834","display_name":"Gaussian binomial coefficient","level":4,"score":0.5010628700256348},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4231472313404083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3471181392669678},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.32856839895248413},{"id":"https://openalex.org/C199335787","wikidata":"https://www.wikidata.org/wiki/Q743364","display_name":"Negative binomial distribution","level":3,"score":0.14857640862464905},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1287420094013214},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12474942207336426},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/1800","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1800","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r47/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/1800","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1800","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v11i1r47/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":null,"license_id":null,"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/W1523717544.pdf","grobid_xml":"https://content.openalex.org/works/W1523717544.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W39064377","https://openalex.org/W154186175","https://openalex.org/W621608175","https://openalex.org/W1990048287","https://openalex.org/W2034445222","https://openalex.org/W2049287010","https://openalex.org/W2051380353","https://openalex.org/W2061138851","https://openalex.org/W2075096616","https://openalex.org/W2134984950","https://openalex.org/W2143349794","https://openalex.org/W2147911079","https://openalex.org/W2914659449"],"related_works":["https://openalex.org/W4225635267","https://openalex.org/W3214798365","https://openalex.org/W2896451556","https://openalex.org/W2058976745","https://openalex.org/W4212980217","https://openalex.org/W2962898873","https://openalex.org/W1619654942","https://openalex.org/W2047523883","https://openalex.org/W4389325763","https://openalex.org/W2266792609"],"abstract_inverted_index":{"We":[0,17],"prove":[1],"a":[2,20],"recent":[3],"conjecture":[4],"of":[5,11,23,39],"Lassalle":[6],"about":[7],"positivity":[8],"and":[9],"integrality":[10],"coefficients":[12,43],"in":[13],"some":[14],"polynomial":[15],"expansions.":[16],"also":[18],"give":[19],"combinatorial":[21],"interpretation":[22],"those":[24],"numbers.":[25],"Finally,":[26],"we":[27],"show":[28],"that":[29],"this":[30],"question":[31],"is":[32],"closely":[33],"related":[34],"to":[35],"the":[36,41],"fundamental":[37],"problem":[38],"calculating":[40],"linearization":[42],"for":[44],"binomial":[45],"coefficients.":[46]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}