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- Ordered_Bell_number 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 are1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247563, ... (sequence A000670 in 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).".
- Ordered_Bell_number thumbnail 13-Weak-Orders.svg?width=300.
- Ordered_Bell_number wikiPageID "6992164".
- Ordered_Bell_number wikiPageRevisionID "596091903".
- Ordered_Bell_number hasPhotoCollection Ordered_Bell_number.
- Ordered_Bell_number subject Category:Enumerative_combinatorics.
- Ordered_Bell_number subject Category:Integer_sequences.
- Ordered_Bell_number comment "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 are1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, 102247563, ...".
- Ordered_Bell_number label "Ordered Bell number".
- Ordered_Bell_number sameAs m.0rphffc.
- Ordered_Bell_number sameAs Q7100706.
- Ordered_Bell_number sameAs Q7100706.
- Ordered_Bell_number wasDerivedFrom Ordered_Bell_number?oldid=596091903.
- Ordered_Bell_number depiction 13-Weak-Orders.svg.
- Ordered_Bell_number isPrimaryTopicOf Ordered_Bell_number.
