Ordered Bell number (original) (raw)
En mathématiques, et plus particulièrement en combinatoire, les nombres de Fubini ou nombres de Bell ordonnés dénombrent les partitions ordonnées d'un ensemble E à n éléments, c'est-à-dire les familles finies de parties non vides disjointes de E dont la réunion est égale à E. Par exemple, pour n = 3, il y a 13 partitions ordonnées de : 6 du type , 3 du type , 3 du type , plus .
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| dbo:abstract | In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the number of weak orderings on a set of n elements (orderings of the elements into a sequence allowing ties, such as might arise as the outcome of a horse race). Starting from n = 0, these numbers are 1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247563, ... (sequence in the OEIS). The ordered Bell numbers may be computed via a summation formula involving binomial coefficients, or by using a recurrence relation. Along with the weak orderings, they count several other types of combinatorial objects that have a bijective correspondence to the weak orderings, such as the ordered multiplicative partitions of a squarefree number or the faces of all dimensions of a permutohedron (e.g. the sum of faces of all dimensions in the truncated octahedron is 1 + 14 + 36 + 24 = 75). (en) En mathématiques, et plus particulièrement en combinatoire, les nombres de Fubini ou nombres de Bell ordonnés dénombrent les partitions ordonnées d'un ensemble E à n éléments, c'est-à-dire les familles finies de parties non vides disjointes de E dont la réunion est égale à E. Par exemple, pour n = 3, il y a 13 partitions ordonnées de : 6 du type , 3 du type , 3 du type , plus . (fr) |
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| rdf:type | yago:Abstraction100002137 yago:Arrangement107938773 yago:Group100031264 yago:Ordering108456993 yago:WikicatIntegerSequences yago:Sequence108459252 yago:Series108457976 |
| rdfs:comment | En mathématiques, et plus particulièrement en combinatoire, les nombres de Fubini ou nombres de Bell ordonnés dénombrent les partitions ordonnées d'un ensemble E à n éléments, c'est-à-dire les familles finies de parties non vides disjointes de E dont la réunion est égale à E. Par exemple, pour n = 3, il y a 13 partitions ordonnées de : 6 du type , 3 du type , 3 du type , plus . (fr) In number theory and enumerative combinatorics, the ordered Bell numbers or Fubini numbers count the number of weak orderings on a set of n elements (orderings of the elements into a sequence allowing ties, such as might arise as the outcome of a horse race). Starting from n = 0, these numbers are 1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247563, ... (sequence in the OEIS). (en) |
| rdfs:label | Nombre de Fubini (fr) Ordered Bell number (en) |
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