@prefix rdf: . @prefix dbr: . @prefix yago: . dbr:Eulerian_number rdf:type yago:Sequence108459252 , yago:WikicatIntegerSequences , yago:WikicatIntegers , yago:Attribute100024264 , yago:Triangle113879320 , yago:WikicatTrianglesOfNumbers , yago:Ordering108456993 , yago:Arrangement107938773 , yago:Number113582013 , yago:Integer113728499 , yago:PlaneFigure113863186 , yago:Figure113862780 , yago:Shape100027807 , yago:Measure100033615 , yago:Polygon113866144 , yago:Abstraction100002137 , yago:Group100031264 , yago:Series108457976 , yago:DefiniteQuantity113576101 . @prefix owl: . dbr:Eulerian_number rdf:type owl:Thing . @prefix rdfs: . dbr:Eulerian_number rdfs:label "Euler-Zahlen"@de , "Eulerian number"@en , "Eulerskt tal"@sv , "Numeri euleriani"@it , "Liczby Eulera"@pl , "\u0427\u0438\u0441\u043B\u0430 \u042D\u0439\u043B\u0435\u0440\u0430 I \u0440\u043E\u0434\u0430"@ru , "\u0427\u0438\u0441\u043B\u0430 \u0415\u0439\u043B\u0435\u0440\u0430 I \u0440\u043E\u0434\u0443"@uk , "Nombre eul\u00E9rien"@fr , "\uC624\uC77C\uB7EC \uC218 (\uC870\uD569\uB860)"@ko ; rdfs:comment "Die nach Leonhard Euler benannte Euler-Zahl An,k in der Kombinatorik, auch geschrieben als oder , ist die Anzahl der Permutationen (Anordnungen) von , in denen genau Elemente gr\u00F6\u00DFer als das vorhergehende sind, die also genau Anstiege enthalten. \u00C4quivalent dazu ist die Definition mit \u201Ekleiner\u201C statt \u201Egr\u00F6\u00DFer\u201C und \u201EAbstiege\u201C statt \u201EAnstiege\u201C. Nach einer anderen Definition ist die Euler-Zahl die Anzahl der Permutationen von mit genau maximalen monoton ansteigenden Abschnitten, wodurch der zweite Parameter gegen\u00FCber der hier verwendeten Definition um eins verschoben ist: ."@de , "( \uC774 \uBB38\uC11C\uB294 \uC870\uD569\uB860\uC758 \uC624\uC77C\uB7EC \uC218(Eulerian number) \uC5D0 \uAD00\uD55C \uAC83\uC785\uB2C8\uB2E4. \uBCA0\uB974\uB204\uC774 \uC218\uC640 \uAD00\uB828\uB41C \uC218\uC5F4\uC5D0 \uB300\uD574\uC11C\uB294 \uC624\uC77C\uB7EC \uC218 \uBB38\uC11C\uB97C \uCC38\uACE0\uD558\uC2ED\uC2DC\uC624.) \uC870\uD569\uB860\uC5D0\uC11C \uC624\uC77C\uB7EC \uC218(Euler\u6578, \uC601\uC5B4: Eulerian number)\uB294 \uC8FC\uC5B4\uC9C4 \uAC1C\uC218\uC758 \uC5ED\uD589\uC744 \uAC00\uC9C0\uB294 \uC21C\uC5F4\uC744 \uC138\uB294 \uC218\uC774\uB2E4."@ko , "En math\u00E9matiques, et plus pr\u00E9cis\u00E9ment en analyse combinatoire, le nombre eul\u00E9rien A(n, k), est le nombre de permutations des entiers de 1 \u00E0 n pour lesquelles exactement k \u00E9l\u00E9ments sont plus grands que l'\u00E9l\u00E9ment pr\u00E9c\u00E9dent (permutations avec k \u00AB mont\u00E9es \u00BB. Les nombres eul\u00E9riens sont les coefficients des polyn\u00F4mes eul\u00E9riens : . Ces polyn\u00F4mes apparaissent au num\u00E9rateur d'expressions li\u00E9es \u00E0 la fonction g\u00E9n\u00E9ratrice de la suite . Ces nombres forment la suite de l'OEIS. Les nombres A(n, k) sont aussi not\u00E9s E(n, k) et"@fr , "In combinatoria, il numero euleriano A(n, m) \u00E8 il numero di permutazioni dei numeri fra 1 e n nelle quali esattamente m elementi sono maggiori di quelli precedenti. Tali numeri sono anche i coefficienti dei polinomi di Eulero: I polinomi di Eulero sono definiti dalla funzione generatrice esponenziale: Essi possono essere calcolati attraverso la seguente formula ricorsiva: Un modo equivalente per dare questa definizione \u00E8 quello di definire i polinomi di Eulero induttivamente: Le notazioni per questi numeri sono A(n, m), E(n, m) e . Essi non vanno confusi con i numeri di Eulero."@it , "\u0412 \u043A\u043E\u043C\u0431\u0456\u043D\u0430\u0442\u043E\u0440\u0438\u0446\u0456 \u0447\u0438\u0441\u043B\u043E\u043C \u0415\u0439\u043B\u0435\u0440\u0430 I \u0440\u043E\u0434\u0443 \u0456\u0437 \u043F\u043E , \u0449\u043E \u043F\u043E\u0437\u043D\u0430\u0447\u0430\u0454\u0442\u044C\u0441\u044F \u0447\u0438 , \u043D\u0430\u0437\u0438\u0432\u0430\u0454\u0442\u044C\u0441\u044F \u043A\u0456\u043B\u044C\u043A\u0456\u0441\u0442\u044C \u043F\u0435\u0440\u0435\u0441\u0442\u0430\u043D\u043E\u0432\u043E\u043A \u043F\u043E\u0440\u044F\u0434\u043A\u0443 \u0437 , \u0442\u043E\u0431\u0442\u043E \u0442\u0430\u043A\u0438\u0445 \u043F\u0435\u0440\u0435\u0441\u0442\u0430\u043D\u043E\u0432\u043E\u043A , \u0449\u043E \u0456\u0441\u043D\u0443\u0454 \u0440\u0456\u0432\u043D\u043E \u0456\u043D\u0434\u0435\u043A\u0441\u0456\u0432 , \u0434\u043B\u044F \u044F\u043A\u0438\u0445 . \u0427\u0438\u0441\u043B\u0430 \u0415\u0439\u043B\u0435\u0440\u0430 I \u0440\u043E\u0434\u0443 \u043C\u0430\u044E\u0442\u044C \u0442\u0430\u043A\u043E\u0436 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u043D\u0443 \u0456 \u0456\u043C\u043E\u0432\u0456\u0440\u043D\u0456\u0441\u043D\u0443 \u0456\u043D\u0442\u0435\u0440\u043F\u0440\u0435\u0442\u0430\u0446\u0456\u044E: \u0447\u0438\u0441\u043B\u043E \u0432\u0438\u0440\u0430\u0436\u0430\u0454 -\u043C\u0456\u0440\u043D\u0438\u0439 \u043E\u0431'\u0454\u043C \u0447\u0430\u0441\u0442\u0438\u043D\u0438 -\u043C\u0456\u0440\u043D\u043E\u0433\u043E \u0433\u0456\u043F\u0435\u0440\u043A\u0443\u0431\u0430, \u043E\u0431\u043C\u0435\u0436\u0435\u043D\u043E\u0433\u043E -\u043C\u0456\u0440\u043D\u0438\u043C\u0438 \u0433\u0456\u043F\u0435\u0440\u043F\u043B\u043E\u0449\u0438\u043D\u0430\u043C\u0438 \u0456 ; \u0432\u043E\u043D\u043E \u0432\u0438\u0440\u0430\u0436\u0430\u0454 \u0456\u043C\u043E\u0432\u0456\u0440\u043D\u0456\u0441\u0442\u044C \u0442\u043E\u0433\u043E, \u0449\u043E \u0441\u0443\u043C\u0430 n \u043D\u0435\u0437\u0430\u043B\u0435\u0436\u043D\u0438\u0445 \u0437\u043C\u0456\u043D\u043D\u0438\u0445 \u0437 \u0440\u0456\u0432\u043D\u043E\u043C\u0456\u0440\u043D\u0438\u043C \u0440\u043E\u0437\u043F\u043E\u0434\u0456\u043B\u043E\u043C \u043D\u0430 \u0432\u0456\u0434\u0440\u0456\u0437\u043A\u0443 \u043B\u0435\u0436\u0438\u0442\u044C \u043C\u0456\u0436 ."@uk , "Ett eulerskt tal E(n, m) \u00E4r inom matematik ett tal som \u00E4r antalet permutationer p\u00E5 m\u00E4ngden {1, 2, ..., n} som har m \"stigningar\". En annan beteckning f\u00F6r E(n, m) \u00E4r ."@sv , "\u0412 \u043A\u043E\u043C\u0431\u0438\u043D\u0430\u0442\u043E\u0440\u0438\u043A\u0435 \u0447\u0438\u0441\u043B\u043E\u043C \u042D\u0439\u043B\u0435\u0440\u0430 I \u0440\u043E\u0434\u0430 \u0438\u0437 n \u043F\u043E k, \u043E\u0431\u043E\u0437\u043D\u0430\u0447\u0430\u0435\u043C\u044B\u043C \u0438\u043B\u0438 , \u043D\u0430\u0437\u044B\u0432\u0430\u0435\u0442\u0441\u044F \u043A\u043E\u043B\u0438\u0447\u0435\u0441\u0442\u0432\u043E \u043F\u0435\u0440\u0435\u0441\u0442\u0430\u043D\u043E\u0432\u043E\u043A \u043F\u043E\u0440\u044F\u0434\u043A\u0430 n \u0441 k \u043F\u043E\u0434\u044A\u0451\u043C\u0430\u043C\u0438, \u0442\u043E \u0435\u0441\u0442\u044C \u0442\u0430\u043A\u0438\u0445 \u043F\u0435\u0440\u0435\u0441\u0442\u0430\u043D\u043E\u0432\u043E\u043A , \u0447\u0442\u043E \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0440\u043E\u0432\u043D\u043E k \u0438\u043D\u0434\u0435\u043A\u0441\u043E\u0432 j, \u0434\u043B\u044F \u043A\u043E\u0442\u043E\u0440\u044B\u0445 . \u0427\u0438\u0441\u043B\u0430 \u042D\u0439\u043B\u0435\u0440\u0430 I \u0440\u043E\u0434\u0430 \u043E\u0431\u043B\u0430\u0434\u0430\u044E\u0442 \u0442\u0430\u043A\u0436\u0435 \u0433\u0435\u043E\u043C\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043A\u043E\u0439 \u0438 \u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u043D\u043E\u0439 \u0438\u043D\u0442\u0435\u0440\u043F\u0440\u0435\u0442\u0430\u0446\u0438\u0435\u0439 \u2014 \u0447\u0438\u0441\u043B\u043E \u0432\u044B\u0440\u0430\u0436\u0430\u0435\u0442: \n* \u043E\u0431\u044A\u0451\u043C \u0447\u0430\u0441\u0442\u0438 n-\u043C\u0435\u0440\u043D\u043E\u0433\u043E \u0433\u0438\u043F\u0435\u0440\u043A\u0443\u0431\u0430, \u043E\u0433\u0440\u0430\u043D\u0438\u0447\u0435\u043D\u043D\u043E\u0433\u043E \u0433\u0438\u043F\u0435\u0440\u043F\u043B\u043E\u0441\u043A\u043E\u0441\u0442\u044F\u043C\u0438 \u0438 ; \n* \u0432\u0435\u0440\u043E\u044F\u0442\u043D\u043E\u0441\u0442\u044C \u0442\u043E\u0433\u043E, \u0447\u0442\u043E \u0441\u0443\u043C\u043C\u0430 n \u043D\u0435\u0437\u0430\u0432\u0438\u0441\u0438\u043C\u044B\u0445 \u0440\u0430\u0432\u043D\u043E\u043C\u0435\u0440\u043D\u043E \u0440\u0430\u0441\u043F\u0440\u0435\u0434\u0435\u043B\u0451\u043D\u043D\u044B\u0445 \u0432 \u043E\u0442\u0440\u0435\u0437\u043A\u0435 \u043F\u0435\u0440\u0435\u043C\u0435\u043D\u043D\u044B\u0445 \u043B\u0435\u0436\u0438\u0442 \u043C\u0435\u0436\u0434\u0443 k-1 \u0438 k."@ru , "Liczby Eulera \u2013 dwa ci\u0105gi liczbowe badane przez Leonarda Eulera."@pl , "In combinatorics, the Eulerian number A(n, m) is the number of permutations of the numbers 1 to n in which exactly m elements are greater than the previous element (permutations with m \"ascents\"). They are the coefficients of the Eulerian polynomials: The Eulerian polynomials are defined by the exponential generating function The Eulerian polynomials can be computed by the recurrence An equivalent way to write this definition is to set the Eulerian polynomials inductively by Other notations for A(n, m) are E(n, m) and ."@en ; owl:differentFrom , dbr:Euler_number . @prefix foaf: . dbr:Eulerian_number foaf:depiction . @prefix dcterms: . @prefix dbc: . dbr:Eulerian_number dcterms:subject dbc:Triangles_of_numbers , dbc:Factorial_and_binomial_topics , dbc:Enumerative_combinatorics , dbc:Integer_sequences . @prefix dbo: . dbr:Eulerian_number dbo:wikiPageID 5041744 ; dbo:wikiPageRevisionID 1113350916 ; dbo:wikiPageWikiLink dbr:Linear_combination , dbr:Iverson_bracket , dbr:Polynomial , dbr:Combinatorics , dbr:Alternating_sum , dbr:Concrete_Mathematics , dbr:Binomial_coefficient , dbr:Bernoulli_number , , dbr:Multiset , dbc:Triangles_of_numbers , dbr:Triangular_array , dbr:Recursion , dbr:Degree_of_a_polynomial , dbr:Aequationes_Mathematicae , dbr:OEIS , dbr:Leonhard_Euler , dbc:Factorial_and_binomial_topics , , dbr:Double_factorial , dbr:Generating_function , dbr:Permutation , dbc:Enumerative_combinatorics , dbc:Integer_sequences , dbr:Factorial . @prefix ns9: . dbr:Eulerian_number dbo:wikiPageExternalLink ns9:Eulerian_polynomials , , , , . @prefix dbpedia-de: . dbr:Eulerian_number owl:sameAs dbpedia-de:Euler-Zahlen , , , . @prefix wikidata: . dbr:Eulerian_number owl:sameAs wikidata:Q1373849 . @prefix yago-res: . dbr:Eulerian_number owl:sameAs yago-res:Eulerian_number . @prefix dbpedia-sv: . dbr:Eulerian_number owl:sameAs dbpedia-sv:Eulerskt_tal . @prefix ns14: . dbr:Eulerian_number owl:sameAs ns14:P2oh . @prefix dbpedia-it: . dbr:Eulerian_number owl:sameAs dbpedia-it:Numeri_euleriani . @prefix dbpedia-pl: . dbr:Eulerian_number owl:sameAs dbpedia-pl:Liczby_Eulera , , . @prefix dbp: . @prefix dbt: . dbr:Eulerian_number dbp:wikiPageUsesTemplate dbt:Use_American_English , dbt:Short_description , dbt:Cite_journal , dbt:Cite_book , dbt:Cite_arXiv , dbt:Math , dbt:MathWorld , dbt:Distinguish , dbt:OEIS , dbt:Diagonal_split_header , dbt:MathPages ; dbo:thumbnail ; dbp:id "home/kmath012/kmath012"@en ; dbp:title "Worpitzky's Identity"@en , "Second-Order Eulerian Triangle"@en , "Eulerian Number"@en , "Eulerian Numbers"@en , "Euler's Number Triangle"@en ; dbp:urlname "EulerianNumber"@en , "WorpitzkysIdentity"@en , "EulersNumberTriangle"@en , "Second-OrderEulerianTriangle"@en ; dbo:abstract "Ett eulerskt tal E(n, m) \u00E4r inom matematik ett tal som \u00E4r antalet permutationer p\u00E5 m\u00E4ngden {1, 2, ..., n} som har m \"stigningar\". En annan beteckning f\u00F6r E(n, m) \u00E4r ."@sv , "Liczby Eulera \u2013 dwa ci\u0105gi liczbowe badane przez Leonarda Eulera."@pl , "( \uC774 \uBB38\uC11C\uB294 \uC870\uD569\uB860\uC758 \uC624\uC77C\uB7EC \uC218(Eulerian number) \uC5D0 \uAD00\uD55C \uAC83\uC785\uB2C8\uB2E4. \uBCA0\uB974\uB204\uC774 \uC218\uC640 \uAD00\uB828\uB41C \uC218\uC5F4\uC5D0 \uB300\uD574\uC11C\uB294 \uC624\uC77C\uB7EC \uC218 \uBB38\uC11C\uB97C \uCC38\uACE0\uD558\uC2ED\uC2DC\uC624.) \uC870\uD569\uB860\uC5D0\uC11C \uC624\uC77C\uB7EC \uC218(Euler\u6578, \uC601\uC5B4: Eulerian number)\uB294 \uC8FC\uC5B4\uC9C4 \uAC1C\uC218\uC758 \uC5ED\uD589\uC744 \uAC00\uC9C0\uB294 \uC21C\uC5F4\uC744 \uC138\uB294 \uC218\uC774\uB2E4."@ko , "En math\u00E9matiques, et plus pr\u00E9cis\u00E9ment en analyse combinatoire, le nombre eul\u00E9rien A(n, k), est le nombre de permutations des entiers de 1 \u00E0 n pour lesquelles exactement k \u00E9l\u00E9ments sont plus grands que l'\u00E9l\u00E9ment pr\u00E9c\u00E9dent (permutations avec k \u00AB mont\u00E9es \u00BB. Les nombres eul\u00E9riens sont les coefficients des polyn\u00F4mes eul\u00E9riens : . Ces polyn\u00F4mes apparaissent au num\u00E9rateur d'expressions li\u00E9es \u00E0 la fonction g\u00E9n\u00E9ratrice de la suite . Ces nombres forment la suite de l'OEIS. Les nombres A(n, k) sont aussi not\u00E9s E(n, k) et"@fr , "In combinatorics, the Eulerian number A(n, m) is the number of permutations of the numbers 1 to n in which exactly m elements are greater than the previous element (permutations with m \"ascents\"). They are the coefficients of the Eulerian polynomials: The Eulerian polynomials are defined by the exponential generating function The Eulerian polynomials can be computed by the recurrence An equivalent way to write this definition is to set the Eulerian polynomials inductively by Other notations for A(n, m) are E(n, m) and ."@en , "In combinatoria, il numero euleriano A(n, m) \u00E8 il numero di permutazioni dei numeri fra 1 e n nelle quali esattamente m elementi sono maggiori di quelli precedenti. Tali numeri sono anche i coefficienti dei polinomi di Eulero: I polinomi di Eulero sono definiti dalla funzione generatrice esponenziale: Essi possono essere calcolati attraverso la seguente formula ricorsiva: Un modo equivalente per dare questa definizione \u00E8 quello di definire i polinomi di Eulero induttivamente: Le notazioni per questi numeri sono A(n, m), E(n, m) e . Essi non vanno confusi con i numeri di Eulero."@it , "Die nach Leonhard Euler benannte Euler-Zahl An,k in der Kombinatorik, auch geschrieben als oder , ist die Anzahl der Permutationen (Anordnungen) von , in denen genau Elemente gr\u00F6\u00DFer als das vorhergehende sind, die also genau Anstiege enthalten. \u00C4quivalent dazu ist die Definition mit \u201Ekleiner\u201C statt \u201Egr\u00F6\u00DFer\u201C und \u201EAbstiege\u201C statt \u201EAnstiege\u201C. 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